gdz.top
Задания, страница 102 - 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 18. Окружность и круг - страница 102.
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" => 1129793 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "102" "field_page_end" => "103" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/samost-18" "field_display_title" => "Задания" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #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 {#1034 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Branch {#1035 #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 {#1038 #items: array:1 [ 0 => App\Models\Term {#1037 #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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 {#1039 #items: array:1 [ 0 => App\Models\Book {#1040 #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 {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #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 [ …10] #original: array:10 [ …10] #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_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 #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 [ …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 } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 #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 [ …6] …17 } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:2 [ 0 => App\Models\Term {#1048 …30} 1 => App\Models\Term {#1049 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1062 #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 {#1063 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1066 #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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1050} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1051} "field_country" => Illuminate\Database\Eloquent\Collection {#1053} "field_city" => Illuminate\Database\Eloquent\Collection {#1055} "field_series" => Illuminate\Database\Eloquent\Collection {#1057} "field_umk" => Illuminate\Database\Eloquent\Collection {#1058} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1059} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1061} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1062} "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 {#1063} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1064} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1065} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1066} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067 #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 {#1038} "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 {#1039} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067} ] #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 {#1138 #items: array:2 [ 0 => App\Models\Branch {#1068 #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 {#1071 #items: array:1 [ 0 => App\Models\Term {#1069 #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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 {#1072 #items: array:1 [ 0 => App\Models\Book {#1073 #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 {#1074 #items: array:1 [ 0 => App\Models\Term {#1075 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:1 [ 0 => App\Models\Term {#1079 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:2 [ 0 => App\Models\Term {#1081 …30} 1 => App\Models\Term {#1082 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Term {#1085 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Term {#1087 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1089 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1095 #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 {#1096 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1099 #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 {#1074} "field_class" => Illuminate\Database\Eloquent\Collection {#1076} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1078} "field_author" => Illuminate\Database\Eloquent\Collection {#1080} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1083} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1084} "field_country" => Illuminate\Database\Eloquent\Collection {#1086} "field_city" => Illuminate\Database\Eloquent\Collection {#1088} "field_series" => Illuminate\Database\Eloquent\Collection {#1090} "field_umk" => Illuminate\Database\Eloquent\Collection {#1091} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1092} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1093} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1094} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1095} "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 {#1096} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1097} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1098} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1099} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1100 #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 {#1071} "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 {#1072} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1100} ] #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 {#1101 #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" => 1129380 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность и круг" "field_branch_order" => "18" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Term {#1103 #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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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" => "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 {#1104 #items: array:1 [ 0 => App\Models\Book {#1105 #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 {#1106 #items: array:1 [ 0 => App\Models\Term {#1107 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Term {#1109 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Term {#1111 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:2 [ 0 => App\Models\Term {#1113 …30} 1 => App\Models\Term {#1114 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1115 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Term {#1117 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Term {#1119 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Term {#1121 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1122 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1126 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1127 #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 {#1128 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1131 #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 {#1106} "field_class" => Illuminate\Database\Eloquent\Collection {#1108} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1110} "field_author" => Illuminate\Database\Eloquent\Collection {#1112} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1115} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1116} "field_country" => Illuminate\Database\Eloquent\Collection {#1118} "field_city" => Illuminate\Database\Eloquent\Collection {#1120} "field_series" => Illuminate\Database\Eloquent\Collection {#1122} "field_umk" => Illuminate\Database\Eloquent\Collection {#1123} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1124} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1125} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1126} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1127} "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 {#1128} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1129} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1130} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1131} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Branch {#1133 #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 {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 …30} ] #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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1105} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137 #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 {#1134} "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1137} ] #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" => 1129380 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность и круг" "field_branch_order" => "18" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1102} "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 {#1104} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132} ] #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 {#1141 #items: array:3 [ 0 => App\Models\Element {#1150 #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" => 1320122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1159 #items: array:1 [ 0 => App\Models\Edition {#1151 #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 {#1153 #items: array:1 [ 0 => App\Models\Term {#1152 …30} ] #escapeWhenCastingToString: false } "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 {#1154 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "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 {#1153} "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 {#1154} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1155} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1156} "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" => "1129793" "type" => "task" ] "text" => "<p><strong>Самостоятельно изобразите круговой сектор.</strong></p><p><strong>Самостоятельно определите, что называется <em>градусной величиной кругового сектора</em>.</strong></p>" "img" => array:2 [ 0 => array:5 [ "name" => "18-1.jpg" "alt" => null "width" => "1193" "height" => 192 "path" => "/media/geometrija_07/Smirnova-u17/0-samost/18-1.webp?ts=1753982503" ] 1 => array:5 [ "name" => "18-2.jpg" "alt" => null "width" => "1780" "height" => 230 "path" => "/media/geometrija_07/Smirnova-u17/0-samost/18-2.webp?ts=1753982503" ] ] ] #original: array:7 [ "id" => 1320122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1159} "task" => array:2 [ "refs" => "1129793" "type" => "task" ] "text" => "<p><strong>Самостоятельно изобразите круговой сектор.</strong></p><p><strong>Самостоятельно определите, что называется <em>градусной величиной кругового сектора</em>.</strong></p>" "img" => array:2 [ 0 => array:5 [ "name" => "18-1.jpg" "alt" => null "width" => "1193" "height" => 192 "path" => "/media/geometrija_07/Smirnova-u17/0-samost/18-1.webp?ts=1753982503" ] 1 => array:5 [ "name" => "18-2.jpg" "alt" => null "width" => "1780" "height" => 230 "path" => "/media/geometrija_07/Smirnova-u17/0-samost/18-2.webp?ts=1753982503" ] ] ] #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 {#1157 #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" => 1320495 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1167 #items: array:1 [ 0 => App\Models\Edition {#1158 #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 {#1161 #items: array:1 [ 0 => App\Models\Term {#1160 …30} ] #escapeWhenCastingToString: false } "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 {#1162 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1163 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1164 #items: [] #escapeWhenCastingToString: false } "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 {#1161} "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 {#1162} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1163} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1164} "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" => "1129793" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "18-1.jpg" "alt" => null "width" => "1430" "height" => 1200 "path" => "/media/geometrija_07/Smirnova-u17/1-samost/18-1.webp?ts=1753982622" ] ] ] #original: array:6 [ "id" => 1320495 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1167} "task" => array:2 [ "refs" => "1129793" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "18-1.jpg" "alt" => null "width" => "1430" "height" => 1200 "path" => "/media/geometrija_07/Smirnova-u17/1-samost/18-1.webp?ts=1753982622" ] ] ] #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 {#1165 #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" => 1541757 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175 #items: array:1 [ 0 => App\Models\Edition {#1166 #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 {#1169 #items: array:1 [ 0 => App\Models\Term {#1168 …30} ] #escapeWhenCastingToString: false } "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 {#1170 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172 #items: [] #escapeWhenCastingToString: false } "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 {#1169} "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 {#1170} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1172} "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" => "1129793" "type" => "task" ] "text" => "<p><strong>Самостоятельно изобразите круговой сектор.</strong></p><p>Круговой сектор — это часть круга, которая ограничена дугой окружности и двумя радиусами, соединяющими концы этой дуги с центром круга. Представьте себе кусок пиццы — это наглядный пример кругового сектора.</p><p>Ниже представлено изображение кругового сектора $OAB$. <svg width="220" height="140" viewBox="0 0 220 140"><title>Круговой сектор</title><path d="M 100,120 L 195,120 A 95,95 0 0 0 100,25 Z" fill="#cceeff" stroke="#333" stroke-width="1.5"></path><circle cx="100" cy="120" r="3" fill="#333"></circle><text x="80" y="125" font-family="Georgia, serif" font-size="18" font-style="italic">O</text><text x="200" y="125" font-family="Georgia, serif" font-size="18" font-style="italic">A</text><text x="95" y="20" font-family="Georgia, serif" font-size="18" font-style="italic">B</text><text x="145" y="110" font-family="Georgia, serif" font-size="18" font-style="italic">R</text><text x="80" y="75" font-family="Georgia, serif" font-size="18" font-style="italic">R</text><path d="M 130,120 A 30,30 0 0 0 100,90" fill="none" stroke="gray" stroke-width="1"></path><text x="118" y="105" font-family="Georgia, serif" font-size="18" font-style="italic">α</text></svg></p><p>На этом рисунке:</p><ul><li>Точка $O$ — центр круга.</li><li>$OA$ и $OB$ — радиусы круга (обозначены как $R$).</li><li>Кривая линия между точками $A$ и $B$ — это дуга окружности.</li><li>Закрашенная область $OAB$ и есть круговой сектор.</li><li>Угол $AOB$, обозначенный греческой буквой $α$ (альфа), — это центральный угол сектора.</li></ul><p>Ответ: Изображение и описание кругового сектора представлены выше.</p><p><strong>Самостоятельно определите, что называется градусной величиной кругового сектора.</strong></p><p>Градусной величиной (или градусной мерой) кругового сектора называется градусная мера соответствующего ему центрального угла. Центральный угол — это угол, вершина которого находится в центре круга, а стороны являются радиусами, ограничивающими данный сектор.</p><p>Проще говоря, "размер" сектора в градусах равен "размеру" угла в его вершине. Если центральный угол $α$ равен, к примеру, $60^\circ$, то и градусная величина кругового сектора тоже равна $60^\circ$.</p><p>Таким образом, градусная величина сектора показывает, какую часть от полного круга ($360^\circ$) он занимает. Например:</p><ul><li>Сектор с центральным углом $90^\circ$ (прямой угол) имеет градусную величину $90^\circ$ и составляет четверть круга.</li><li>Полукруг — это сектор с центральным углом $180^\circ$ (развернутый угол), и его градусная величина равна $180^\circ$.</li><li>Полный круг можно рассматривать как сектор, у которого радиусы совпадают, а угол равен $360^\circ$.</li></ul><p>Ответ: Градусная величина кругового сектора — это величина в градусах центрального угла, который образован двумя радиусами, ограничивающими этот сектор.</p>" ] #original: array:6 [ "id" => 1541757 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1175} "task" => array:2 [ "refs" => "1129793" "type" => "task" ] "text" => "<p><strong>Самостоятельно изобразите круговой сектор.</strong></p><p>Круговой сектор — это часть круга, которая ограничена дугой окружности и двумя радиусами, соединяющими концы этой дуги с центром круга. Представьте себе кусок пиццы — это наглядный пример кругового сектора.</p><p>Ниже представлено изображение кругового сектора $OAB$. <svg width="220" height="140" viewBox="0 0 220 140"><title>Круговой сектор</title><path d="M 100,120 L 195,120 A 95,95 0 0 0 100,25 Z" fill="#cceeff" stroke="#333" stroke-width="1.5"></path><circle cx="100" cy="120" r="3" fill="#333"></circle><text x="80" y="125" font-family="Georgia, serif" font-size="18" font-style="italic">O</text><text x="200" y="125" font-family="Georgia, serif" font-size="18" font-style="italic">A</text><text x="95" y="20" font-family="Georgia, serif" font-size="18" font-style="italic">B</text><text x="145" y="110" font-family="Georgia, serif" font-size="18" font-style="italic">R</text><text x="80" y="75" font-family="Georgia, serif" font-size="18" font-style="italic">R</text><path d="M 130,120 A 30,30 0 0 0 100,90" fill="none" stroke="gray" stroke-width="1"></path><text x="118" y="105" font-family="Georgia, serif" font-size="18" font-style="italic">α</text></svg></p><p>На этом рисунке:</p><ul><li>Точка $O$ — центр круга.</li><li>$OA$ и $OB$ — радиусы круга (обозначены как $R$).</li><li>Кривая линия между точками $A$ и $B$ — это дуга окружности.</li><li>Закрашенная область $OAB$ и есть круговой сектор.</li><li>Угол $AOB$, обозначенный греческой буквой $α$ (альфа), — это центральный угол сектора.</li></ul><p>Ответ: Изображение и описание кругового сектора представлены выше.</p><p><strong>Самостоятельно определите, что называется градусной величиной кругового сектора.</strong></p><p>Градусной величиной (или градусной мерой) кругового сектора называется градусная мера соответствующего ему центрального угла. Центральный угол — это угол, вершина которого находится в центре круга, а стороны являются радиусами, ограничивающими данный сектор.</p><p>Проще говоря, "размер" сектора в градусах равен "размеру" угла в его вершине. Если центральный угол $α$ равен, к примеру, $60^\circ$, то и градусная величина кругового сектора тоже равна $60^\circ$.</p><p>Таким образом, градусная величина сектора показывает, какую часть от полного круга ($360^\circ$) он занимает. Например:</p><ul><li>Сектор с центральным углом $90^\circ$ (прямой угол) имеет градусную величину $90^\circ$ и составляет четверть круга.</li><li>Полукруг — это сектор с центральным углом $180^\circ$ (развернутый угол), и его градусная величина равна $180^\circ$.</li><li>Полный круг можно рассматривать как сектор, у которого радиусы совпадают, а угол равен $360^\circ$.</li></ul><p>Ответ: Градусная величина кругового сектора — это величина в градусах центрального угла, который образован двумя радиусами, ограничивающими этот сектор.</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" => "1129794" "type" => "task" ] "previous" => array:2 [ "refs" => "1129792" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1194 #items: array:1 [ 0 => App\Models\Book {#1147 #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 {#1140 #items: array:1 [ 0 => App\Models\Term {#1139 #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 [ "field_accusative_case" => "геометрию" "field_creative_case" => "геометрией" "field_dative_case" => "геометрии" "field_genitive_case" => "геометрии" "field_nominative_case" => "геометрия" "field_prepositional_case" => "геометрии" ] "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 [ "field_accusative_case" => "геометрию" "field_creative_case" => "геометрией" "field_dative_case" => "геометрии" "field_genitive_case" => "геометрии" "field_nominative_case" => "геометрия" "field_prepositional_case" => "геометрии" ] "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 {#1146 #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:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "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 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" "field_dative_case" => "седьмому" "field_genitive_case" => "седьмого" "field_nominative_case" => "седьмой" "field_prepositional_case" => "седьмом" ] "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 {#1144 #items: array:1 [ 0 => App\Models\Term {#1142 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1145 #items: array:2 [ 0 => App\Models\Term {#1143 #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 {#1173 #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 {#1174 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1176 #items: array:1 [ 0 => App\Models\Term {#1177 #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 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "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 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "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 {#1178 #items: array:1 [ 0 => App\Models\Term {#1179 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1180 #items: array:1 [ 0 => App\Models\Term {#1181 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1182 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1183 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1184 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1185 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1186 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1187 #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 {#1188 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189 #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 {#1140} "field_class" => Illuminate\Database\Eloquent\Collection {#1146} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1144} "field_author" => Illuminate\Database\Eloquent\Collection {#1145} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1174} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1176} "field_country" => Illuminate\Database\Eloquent\Collection {#1178} "field_city" => Illuminate\Database\Eloquent\Collection {#1180} "field_series" => Illuminate\Database\Eloquent\Collection {#1182} "field_umk" => Illuminate\Database\Eloquent\Collection {#1183} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1184} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1185} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1186} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1187} "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 {#1188} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1189} "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 {#1208 #items: array:1 [ 0 => App\Models\BookPage {#1207 #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" => 1114419 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "102" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-102" "field_display_title" => "102" "field_folder" => "1" "field_image_name" => "102" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1209 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1210 #items: array:1 [ 0 => App\Models\Book {#1147} ] #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 {#1211 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Element {#1220 #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" => 1290606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:1 [ 0 => App\Models\Edition {#1151} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1114419" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "102-1.jpg" "alt" => null "width" => "1935" "height" => 2838 "path" => "/media/geometrija_07/Smirnova-u17/0-1/102-1.webp?ts=1753260190" ] ] ] #original: array:6 [ "id" => 1290606 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1222} "book_page" => array:2 [ "refs" => "1114419" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "102-1.jpg" "alt" => null "width" => "1935" "height" => 2838 "path" => "/media/geometrija_07/Smirnova-u17/0-1/102-1.webp?ts=1753260190" ] ] ] #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" => "1114420" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114418" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Task {#1030} ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1114419 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "102" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-102" "field_display_title" => "102" "field_folder" => "1" "field_image_name" => "102" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1209} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1210} "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 {#1211} "content" => Illuminate\Database\Eloquent\Collection {#1221} "next" => array:2 [ "refs" => "1114420" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114418" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1213} ] #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" => 1129793 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "102" "field_page_end" => "103" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/samost-18" "field_display_title" => "Задания" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036} "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 {#1034} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1070} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1138} "content" => Illuminate\Database\Eloquent\Collection {#1141} "next" => array:2 [ "refs" => "1129794" "type" => "task" ] "previous" => array:2 [ "refs" => "1129792" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1194} "page" => array:2 [ "refs" => "1114419" "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 => "*" ] }
Задания (с. 102)
Условие. Задания (с. 102)
скриншот условия
Самостоятельно изобразите круговой сектор.
Самостоятельно определите, что называется градусной величиной кругового сектора.
Решение. Задания (с. 102)
Решение 2. Задания (с. 102)
Самостоятельно изобразите круговой сектор.
Круговой сектор — это часть круга, которая ограничена дугой окружности и двумя радиусами, соединяющими концы этой дуги с центром круга. Представьте себе кусок пиццы — это наглядный пример кругового сектора.
Ниже представлено изображение кругового сектора $OAB$.
На этом рисунке:
- Точка $O$ — центр круга.
- $OA$ и $OB$ — радиусы круга (обозначены как $R$).
- Кривая линия между точками $A$ и $B$ — это дуга окружности.
- Закрашенная область $OAB$ и есть круговой сектор.
- Угол $AOB$, обозначенный греческой буквой $α$ (альфа), — это центральный угол сектора.
Ответ: Изображение и описание кругового сектора представлены выше.
Самостоятельно определите, что называется градусной величиной кругового сектора.
Градусной величиной (или градусной мерой) кругового сектора называется градусная мера соответствующего ему центрального угла. Центральный угол — это угол, вершина которого находится в центре круга, а стороны являются радиусами, ограничивающими данный сектор.
Проще говоря, "размер" сектора в градусах равен "размеру" угла в его вершине. Если центральный угол $α$ равен, к примеру, $60^\circ$, то и градусная величина кругового сектора тоже равна $60^\circ$.
Таким образом, градусная величина сектора показывает, какую часть от полного круга ($360^\circ$) он занимает. Например:
- Сектор с центральным углом $90^\circ$ (прямой угол) имеет градусную величину $90^\circ$ и составляет четверть круга.
- Полукруг — это сектор с центральным углом $180^\circ$ (развернутый угол), и его градусная величина равна $180^\circ$.
- Полный круг можно рассматривать как сектор, у которого радиусы совпадают, а угол равен $360^\circ$.
Ответ: Градусная величина кругового сектора — это величина в градусах центрального угла, который образован двумя радиусами, ограничивающими этот сектор.
Другие задания:
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