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Номер 20.4, страница 116 - гдз по геометрии 7 класс учебник Смирнов, Туяков
Авторы: Смирнов В. А., Туяков Е. А.
Тип: Учебник
Издательство: Мектеп
Год издания: 2017 - 2026
ISBN: 978-601-07-0873-0
Утверждено Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 7 классе
Глава 4. Окружность. Геометрические построения. Параграф 20. Взаимное расположение двух окружностей - номер 20.4, страница 116.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129842 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "116" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/20-4" "field_display_title" => "20.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129379 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "101" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129379 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "101" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:2 [ 0 => App\Models\Branch {#1069 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129379 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Term {#1070 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "101" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Book {#1074 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1087 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129379 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_page_start" => "101" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1073} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1102 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129382 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Взаимное расположение двух окружностей" "field_branch_order" => "20" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Term {#1104 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "112" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1106 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1111 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1111 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1134 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129379 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "101" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1137 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1138 …2} ] #original: array:24 [ "id" => 1129379 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_page_start" => "101" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1137 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1138 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129382 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Взаимное расположение двух окружностей" "field_branch_order" => "20" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_page_start" => "112" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1105} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:3 [ 0 => App\Models\Element {#1167 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1319953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1176 #items: array:1 [ 0 => App\Models\Edition {#1168 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5009 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5009 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1129842" "type" => "task" ] "text" => "<p><strong>20.4.</strong> Расстояние между центрами двух окружностей равно 2 см. Как расположены эти окружности по отношению друг к другу, если их радиусы равны:</p><p><strong>а)</strong> 3 см и 5 см;</p><p><strong>б)</strong> 2 см и 5 см?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1766" "height" => 270 "path" => "/media/geometrija_07/Smirnova-u17/0-20/4-1.webp?ts=1753982457" ] ] ] #original: array:7 [ "id" => 1319953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1176} "task" => array:2 [ "refs" => "1129842" "type" => "task" ] "text" => "<p><strong>20.4.</strong> Расстояние между центрами двух окружностей равно 2 см. Как расположены эти окружности по отношению друг к другу, если их радиусы равны:</p><p><strong>а)</strong> 3 см и 5 см;</p><p><strong>б)</strong> 2 см и 5 см?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1766" "height" => 270 "path" => "/media/geometrija_07/Smirnova-u17/0-20/4-1.webp?ts=1753982457" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1174 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1320409 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1184 #items: array:1 [ 0 => App\Models\Edition {#1175 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5010 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5010 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1181 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1129842" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1465" "height" => 793 "path" => "/media/geometrija_07/Smirnova-u17/1-20/4-1.webp?ts=1753982572" ] ] ] #original: array:6 [ "id" => 1320409 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1184} "task" => array:2 [ "refs" => "1129842" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1465" "height" => 793 "path" => "/media/geometrija_07/Smirnova-u17/1-20/4-1.webp?ts=1753982572" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1182 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1541671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1192 #items: array:1 [ 0 => App\Models\Edition {#1183 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5631 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1189 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5631 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1189 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1129842" "type" => "task" ] "text" => "<p>Для определения взаимного расположения двух окружностей необходимо сравнить расстояние между их центрами ($d$) с суммой ($R_1 + R_2$) и разностью ($|R_1 - R_2|$) их радиусов.По условию, расстояние между центрами $d = 2$ см.</p><p><strong>а)</strong> Радиусы окружностей равны $R_1 = 5$ см и $R_2 = 3$ см.</p><p><strong>1.</strong> Найдём сумму радиусов:<br>$R_1 + R_2 = 5 \text{ см} + 3 \text{ см} = 8 \text{ см}$.</p><p><strong>2.</strong> Найдём разность радиусов:<br>$|R_1 - R_2| = |5 \text{ см} - 3 \text{ см}| = 2 \text{ см}$.</p><p>Сравним расстояние между центрами $d$ с полученными значениями. Мы видим, что расстояние между центрами равно разности радиусов: $d = |R_1 - R_2|$, так как $2 \text{ см} = 2 \text{ см}$.Такое соотношение означает, что окружности касаются внутренним образом. Это значит, что у них есть одна общая точка, и меньшая окружность находится внутри большей.</p><svg width="250" height="150" viewBox="-6 -6 12 12" xmlns="http://www.w3.org/2000/svg"><style> .c1 { stroke: blue; stroke-width: 0.1; fill: rgba(0,0,255,0.1); } .c2 { stroke: red; stroke-width: 0.1; fill: rgba(255,0,0,0.1); } .line { stroke: black; stroke-width: 0.05; } .dot { fill: black; } .lbl { font-family: 'Times New Roman', serif; font-size: 0.8px; text-anchor: middle; } .lbl-sub { font-size: 0.6px; baseline-shift: sub; } </style><circle class="c1" cx="0" cy="0" r="5"></circle><circle class="c2" cx="2" cy="0" r="3"></circle><line class="line" x1="0" y1="0" x2="2" y2="0"></line><circle class="dot" cx="0" cy="0" r="0.1"></circle><circle class="dot" cx="2" cy="0" r="0.1"></circle><text x="-0.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">1</tspan></text><text x="1.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">2</tspan></text><line x1="0" y1="-0.5" x2="2" y2="-0.5" stroke="black" stroke-width="0.05"></line><line x1="0" y1="-0.7" x2="0" y2="-0.3" stroke="black" stroke-width="0.05"></line><line x1="2" y1="-0.7" x2="2" y2="-0.3" stroke="black" stroke-width="0.05"></line><text x="1" y="-1" class="lbl">d=2</text><line x1="0" y1="0.5" x2="5" y2="0.5" stroke="blue" stroke-width="0.05"></line><line x1="0" y1="0.3" x2="0" y2="0.7" stroke="blue" stroke-width="0.05"></line><line x1="5" y1="0.3" x2="5" y2="0.7" stroke="blue" stroke-width="0.05"></line><text x="2.5" y="1.2" class="lbl" fill="blue">R<tspan class="lbl-sub">1</tspan>=5</text><line x1="2" y1="-1.5" x2="5" y2="-1.5" stroke="red" stroke-width="0.05"></line><line x1="2" y1="-1.7" x2="2" y2="-1.3" stroke="red" stroke-width="0.05"></line><line x1="5" y1="-1.7" x2="5" y2="-1.3" stroke="red" stroke-width="0.05"></line><text x="3.5" y="-2.2" class="lbl" fill="red">R<tspan class="lbl-sub">2</tspan>=3</text></svg><p><strong>Ответ:</strong> окружности касаются внутренним образом.</p><p><strong>б)</strong> Радиусы окружностей равны $R_1 = 5$ см и $R_2 = 2$ см.</p><p><strong>1.</strong> Найдём сумму радиусов:<br>$R_1 + R_2 = 5 \text{ см} + 2 \text{ см} = 7 \text{ см}$.</p><p><strong>2.</strong> Найдём разность радиусов:<br>$|R_1 - R_2| = |5 \text{ см} - 2 \text{ см}| = 3 \text{ см}$.</p><p>Сравним расстояние между центрами $d$ с полученными значениями. Мы видим, что расстояние между центрами меньше разности радиусов: $d < |R_1 - R_2|$, так как $2 \text{ см} < 3 \text{ см}$.Это означает, что одна окружность полностью расположена внутри другой, и они не имеют общих точек (не касаются и не пересекаются).</p><svg width="250" height="150" viewBox="-6 -6 12 12" xmlns="http://www.w3.org/2000/svg"><style> .c1 { stroke: blue; stroke-width: 0.1; fill: rgba(0,0,255,0.1); } .c2 { stroke: red; stroke-width: 0.1; fill: rgba(255,0,0,0.1); } .line { stroke: black; stroke-width: 0.05; } .dot { fill: black; } .lbl { font-family: 'Times New Roman', serif; font-size: 0.8px; text-anchor: middle; } .lbl-sub { font-size: 0.6px; baseline-shift: sub; } </style><circle class="c1" cx="0" cy="0" r="5"></circle><circle class="c2" cx="2" cy="0" r="2"></circle><line class="line" x1="0" y1="0" x2="2" y2="0"></line><circle class="dot" cx="0" cy="0" r="0.1"></circle><circle class="dot" cx="2" cy="0" r="0.1"></circle><text x="-0.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">1</tspan></text><text x="1.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">2</tspan></text><line x1="0" y1="0.5" x2="2" y2="0.5" stroke="black" stroke-width="0.05"></line><line x1="0" y1="0.3" x2="0" y2="0.7" stroke="black" stroke-width="0.05"></line><line x1="2" y1="0.3" x2="2" y2="0.7" stroke="black" stroke-width="0.05"></line><text x="1" y="1.2" class="lbl">d=2</text><line x1="0" y1="-0.5" x2="5" y2="-0.5" stroke="blue" stroke-width="0.05"></line><line x1="0" y1="-0.7" x2="0" y2="-0.3" stroke="blue" stroke-width="0.05"></line><line x1="5" y1="-0.7" x2="5" y2="-0.3" stroke="blue" stroke-width="0.05"></line><text x="2.5" y="-1.2" class="lbl" fill="blue">R<tspan class="lbl-sub">1</tspan>=5</text><line x1="2" y1="1" x2="4" y2="1" stroke="red" stroke-width="0.05"></line><line x1="2" y1="0.8" x2="2" y2="1.2" stroke="red" stroke-width="0.05"></line><line x1="4" y1="0.8" x2="4" y2="1.2" stroke="red" stroke-width="0.05"></line><text x="3" y="1.7" class="lbl" fill="red">R<tspan class="lbl-sub">2</tspan>=2</text></svg><p><strong>Ответ:</strong> одна окружность расположена внутри другой, и они не пересекаются.</p>" ] #original: array:6 [ "id" => 1541671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1192} "task" => array:2 [ "refs" => "1129842" "type" => "task" ] "text" => "<p>Для определения взаимного расположения двух окружностей необходимо сравнить расстояние между их центрами ($d$) с суммой ($R_1 + R_2$) и разностью ($|R_1 - R_2|$) их радиусов.По условию, расстояние между центрами $d = 2$ см.</p><p><strong>а)</strong> Радиусы окружностей равны $R_1 = 5$ см и $R_2 = 3$ см.</p><p><strong>1.</strong> Найдём сумму радиусов:<br>$R_1 + R_2 = 5 \text{ см} + 3 \text{ см} = 8 \text{ см}$.</p><p><strong>2.</strong> Найдём разность радиусов:<br>$|R_1 - R_2| = |5 \text{ см} - 3 \text{ см}| = 2 \text{ см}$.</p><p>Сравним расстояние между центрами $d$ с полученными значениями. Мы видим, что расстояние между центрами равно разности радиусов: $d = |R_1 - R_2|$, так как $2 \text{ см} = 2 \text{ см}$.Такое соотношение означает, что окружности касаются внутренним образом. Это значит, что у них есть одна общая точка, и меньшая окружность находится внутри большей.</p><svg width="250" height="150" viewBox="-6 -6 12 12" xmlns="http://www.w3.org/2000/svg"><style> .c1 { stroke: blue; stroke-width: 0.1; fill: rgba(0,0,255,0.1); } .c2 { stroke: red; stroke-width: 0.1; fill: rgba(255,0,0,0.1); } .line { stroke: black; stroke-width: 0.05; } .dot { fill: black; } .lbl { font-family: 'Times New Roman', serif; font-size: 0.8px; text-anchor: middle; } .lbl-sub { font-size: 0.6px; baseline-shift: sub; } </style><circle class="c1" cx="0" cy="0" r="5"></circle><circle class="c2" cx="2" cy="0" r="3"></circle><line class="line" x1="0" y1="0" x2="2" y2="0"></line><circle class="dot" cx="0" cy="0" r="0.1"></circle><circle class="dot" cx="2" cy="0" r="0.1"></circle><text x="-0.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">1</tspan></text><text x="1.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">2</tspan></text><line x1="0" y1="-0.5" x2="2" y2="-0.5" stroke="black" stroke-width="0.05"></line><line x1="0" y1="-0.7" x2="0" y2="-0.3" stroke="black" stroke-width="0.05"></line><line x1="2" y1="-0.7" x2="2" y2="-0.3" stroke="black" stroke-width="0.05"></line><text x="1" y="-1" class="lbl">d=2</text><line x1="0" y1="0.5" x2="5" y2="0.5" stroke="blue" stroke-width="0.05"></line><line x1="0" y1="0.3" x2="0" y2="0.7" stroke="blue" stroke-width="0.05"></line><line x1="5" y1="0.3" x2="5" y2="0.7" stroke="blue" stroke-width="0.05"></line><text x="2.5" y="1.2" class="lbl" fill="blue">R<tspan class="lbl-sub">1</tspan>=5</text><line x1="2" y1="-1.5" x2="5" y2="-1.5" stroke="red" stroke-width="0.05"></line><line x1="2" y1="-1.7" x2="2" y2="-1.3" stroke="red" stroke-width="0.05"></line><line x1="5" y1="-1.7" x2="5" y2="-1.3" stroke="red" stroke-width="0.05"></line><text x="3.5" y="-2.2" class="lbl" fill="red">R<tspan class="lbl-sub">2</tspan>=3</text></svg><p><strong>Ответ:</strong> окружности касаются внутренним образом.</p><p><strong>б)</strong> Радиусы окружностей равны $R_1 = 5$ см и $R_2 = 2$ см.</p><p><strong>1.</strong> Найдём сумму радиусов:<br>$R_1 + R_2 = 5 \text{ см} + 2 \text{ см} = 7 \text{ см}$.</p><p><strong>2.</strong> Найдём разность радиусов:<br>$|R_1 - R_2| = |5 \text{ см} - 2 \text{ см}| = 3 \text{ см}$.</p><p>Сравним расстояние между центрами $d$ с полученными значениями. Мы видим, что расстояние между центрами меньше разности радиусов: $d < |R_1 - R_2|$, так как $2 \text{ см} < 3 \text{ см}$.Это означает, что одна окружность полностью расположена внутри другой, и они не имеют общих точек (не касаются и не пересекаются).</p><svg width="250" height="150" viewBox="-6 -6 12 12" xmlns="http://www.w3.org/2000/svg"><style> .c1 { stroke: blue; stroke-width: 0.1; fill: rgba(0,0,255,0.1); } .c2 { stroke: red; stroke-width: 0.1; fill: rgba(255,0,0,0.1); } .line { stroke: black; stroke-width: 0.05; } .dot { fill: black; } .lbl { font-family: 'Times New Roman', serif; font-size: 0.8px; text-anchor: middle; } .lbl-sub { font-size: 0.6px; baseline-shift: sub; } </style><circle class="c1" cx="0" cy="0" r="5"></circle><circle class="c2" cx="2" cy="0" r="2"></circle><line class="line" x1="0" y1="0" x2="2" y2="0"></line><circle class="dot" cx="0" cy="0" r="0.1"></circle><circle class="dot" cx="2" cy="0" r="0.1"></circle><text x="-0.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">1</tspan></text><text x="1.5" y="-0.2" class="lbl">O<tspan class="lbl-sub">2</tspan></text><line x1="0" y1="0.5" x2="2" y2="0.5" stroke="black" stroke-width="0.05"></line><line x1="0" y1="0.3" x2="0" y2="0.7" stroke="black" stroke-width="0.05"></line><line x1="2" y1="0.3" x2="2" y2="0.7" stroke="black" stroke-width="0.05"></line><text x="1" y="1.2" class="lbl">d=2</text><line x1="0" y1="-0.5" x2="5" y2="-0.5" stroke="blue" stroke-width="0.05"></line><line x1="0" y1="-0.7" x2="0" y2="-0.3" stroke="blue" stroke-width="0.05"></line><line x1="5" y1="-0.7" x2="5" y2="-0.3" stroke="blue" stroke-width="0.05"></line><text x="2.5" y="-1.2" class="lbl" fill="blue">R<tspan class="lbl-sub">1</tspan>=5</text><line x1="2" y1="1" x2="4" y2="1" stroke="red" stroke-width="0.05"></line><line x1="2" y1="0.8" x2="2" y2="1.2" stroke="red" stroke-width="0.05"></line><line x1="4" y1="0.8" x2="4" y2="1.2" stroke="red" stroke-width="0.05"></line><text x="3" y="1.7" class="lbl" fill="red">R<tspan class="lbl-sub">2</tspan>=2</text></svg><p><strong>Ответ:</strong> одна окружность расположена внутри другой, и они не пересекаются.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1129843" "type" => "task" ] "previous" => array:2 [ "refs" => "1129841" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1164 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1149 #items: array:1 [ 0 => App\Models\Term {#1148 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6477 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #original: array:10 [ "id" => 6477 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Term {#1155 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ 0 => App\Models\Term {#1153 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ …6] "field_translit" => "mektep" ] #original: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ …6] "field_translit" => "mektep" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1151 #items: array:2 [ 0 => App\Models\Term {#1152 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Смирнов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Смирнов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7017 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Туяков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Есенкельды" "field_patronymic" => "Алыбаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7017 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Туяков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Есенкельды" "field_patronymic" => "Алыбаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1147 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Term {#1145 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Term {#1144 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1163 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1165 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1162 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1191 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1149} "field_class" => Illuminate\Database\Eloquent\Collection {#1150} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1154} "field_author" => Illuminate\Database\Eloquent\Collection {#1151} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1142} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_country" => Illuminate\Database\Eloquent\Collection {#1146} "field_city" => Illuminate\Database\Eloquent\Collection {#1143} "field_series" => Illuminate\Database\Eloquent\Collection {#1158} "field_umk" => Illuminate\Database\Eloquent\Collection {#1156} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1163} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1165} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1161} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1159} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1162} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1160} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1190} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1191} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1378 #items: array:1 [ 0 => App\Models\BookPage {#328 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1114433 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "116" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-116" "field_display_title" => "116" "field_folder" => "1" "field_image_name" => "116" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1026 #items: array:1 [ 0 => App\Models\Book {#1193 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1217 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1220 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1194 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] …12 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1221 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:1 [ 0 => App\Models\Element {#1223 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1114434" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114432" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:9 [ 0 => App\Models\Task {#1232 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1271 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1285 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1298 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1311 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false 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#classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1350 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 8 => App\Models\Task {#1363 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1114433 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "116" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-116" "field_display_title" => "116" "field_folder" => "1" "field_image_name" => "116" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1026} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1221} "content" => Illuminate\Database\Eloquent\Collection {#1222} "next" => array:2 [ "refs" => "1114434" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114432" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1231} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129842 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "116" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/20-4" "field_display_title" => "20.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1139} "content" => Illuminate\Database\Eloquent\Collection {#1157} "next" => array:2 [ "refs" => "1129843" "type" => "task" ] "previous" => array:2 [ "refs" => "1129841" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195} "page" => array:2 [ "refs" => "1114433" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№20.4 (с. 116)
Условие. №20.4 (с. 116)
скриншот условия
20.4. Расстояние между центрами двух окружностей равно 2 см. Как расположены эти окружности по отношению друг к другу, если их радиусы равны:
а) 3 см и 5 см;
б) 2 см и 5 см?
Решение. №20.4 (с. 116)
Решение 2. №20.4 (с. 116)
Для определения взаимного расположения двух окружностей необходимо сравнить расстояние между их центрами ($d$) с суммой ($R_1 + R_2$) и разностью ($|R_1 - R_2|$) их радиусов.По условию, расстояние между центрами $d = 2$ см.
а) Радиусы окружностей равны $R_1 = 5$ см и $R_2 = 3$ см.
1. Найдём сумму радиусов:
$R_1 + R_2 = 5 \text{ см} + 3 \text{ см} = 8 \text{ см}$.
2. Найдём разность радиусов:
$|R_1 - R_2| = |5 \text{ см} - 3 \text{ см}| = 2 \text{ см}$.
Сравним расстояние между центрами $d$ с полученными значениями. Мы видим, что расстояние между центрами равно разности радиусов: $d = |R_1 - R_2|$, так как $2 \text{ см} = 2 \text{ см}$.Такое соотношение означает, что окружности касаются внутренним образом. Это значит, что у них есть одна общая точка, и меньшая окружность находится внутри большей.
Ответ: окружности касаются внутренним образом.
б) Радиусы окружностей равны $R_1 = 5$ см и $R_2 = 2$ см.
1. Найдём сумму радиусов:
$R_1 + R_2 = 5 \text{ см} + 2 \text{ см} = 7 \text{ см}$.
2. Найдём разность радиусов:
$|R_1 - R_2| = |5 \text{ см} - 2 \text{ см}| = 3 \text{ см}$.
Сравним расстояние между центрами $d$ с полученными значениями. Мы видим, что расстояние между центрами меньше разности радиусов: $d < |R_1 - R_2|$, так как $2 \text{ см} < 3 \text{ см}$.Это означает, что одна окружность полностью расположена внутри другой, и они не имеют общих точек (не касаются и не пересекаются).
Ответ: одна окружность расположена внутри другой, и они не пересекаются.
Другие задания:
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