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Номер 614, страница 158 - гдз по геометрии 7 класс учебник Мерзляк, Полонский
Авторы: Мерзляк А. Г., Полонский В. Б., Якир М. С.
Тип: Учебник
Издательство: Просвещение, Вентана-граф
Год издания: 2023 - 2026
Цвет обложки: оранжевый с графиком
ISBN: 978-5-09-105805-5
Популярные ГДЗ в 7 классе
Глава 4. Окружность и круг. Геометрические построения. Параграф 22. Описанная и вписанная окружности треугольника. Упражнения - номер 614, страница 158.
App\Models\Task {#1024 // 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" => 600361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "158" "field_page_end" => null "field_url" => "/7-klass/geometrija/merzlyak-fgos/614" "field_display_title" => "614" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 599548 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность и круг. Геометрические построения" "field_branch_order" => "4" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #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" => "140" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 904 "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 {#1034 #items: array:2 [ 0 => App\Models\Term {#1035 #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] } 1 => 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: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 {#1037 #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: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 {#1039 #items: array:2 [ 0 => App\Models\Term {#1040 #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] } 1 => App\Models\Term {#1041 #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_author" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:3 [ 0 => App\Models\Term {#1043 #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 [ …12] #original: array:12 [ …12] #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\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:12 [ …12] #original: array:12 [ …12] #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\Term {#1045 #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 [ …12] #original: array:12 [ …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_author_foreign" => Illuminate\Database\Eloquent\Collection {#1046 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ 0 => App\Models\Term {#1048 #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_country" => Illuminate\Database\Eloquent\Collection {#1049 #items: array:1 [ 0 => App\Models\Term {#1050 #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_city" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #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_series" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:2 [ 0 => App\Models\Term {#1057 #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] } 1 => App\Models\Term {#1058 #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_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #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 [ …12] #original: array:12 [ …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_under_the_edition_degree" => null "field_cover_description" => "с графиком" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1017" "field_priority" => "6" "field_default_folder" => "/geometrija_07/merzlyak-u23/" "field_isbn" => "978-5-09-105805-5" "field_cover" => array:1 [ 0 => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" "alt" => "" "width" => "2277" "height" => "3035" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/merzlyak-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ 0 => App\Models\Term {#1066 #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_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2>Нужно ли изучать геометрию? </h2> <p> В седьмом классе учебные нагрузки возрастут. В расписании школьников появится такой предмет как геометрия. Поначалу новая наука вызывает искренний интерес, но уже через некоторое время ребята начинают испытывать трудности при ее освоении. Многие пытаются мотивировать нежелание делать уроки высказываниями вроде: «Да зачем она нужна?», «В жизни такое точно не пригодится», и т.д. Тем не менее оценки по предмету самым прямым образом влияют на общую успеваемость. С помощью «<strong>ГДЗ по Геометрии 7 класс Учебник Мерзляк, Полонский, Якир (Вентана-Граф)</strong>» можно разобраться в аспектах дисциплины и осознать ее смысл. </p> <p> Давайте рассмотрим, какие качества позволяет развить геометрия у учеников: <ol> <li>Логическое, образное мышление.</li> <li>Пространственное представление.</li> <li>Интуитивную и символическую умственную деятельность.</li> <li>Фантазию.</li> <li>Умение анализировать.</li> <li>Грамотную речь.</li> </ol> <p> Основное, что требуется от учащихся на уроках - внимательность. Иначе будет трудно понять, каким образом знание теорем поможет справиться с выполнением задач. Геометрия - наука сугубо практическая, поэтому учителя показывают наглядные примеры во время занятий. Но иногда у подростков все равно остаются вопросы, ответить на которые зачастую некому. Решебник позволит полноценно освоить новую тему и приобрести важные навыки. </p> <h2> Почему ученики выбирают ГДЗ к учебнику Мерзляка? </h2> <p> Учебники подчас содержат очень мало полезных сведений. Возникает ощущение, что авторы этих пособий сосредоточены только на написании разнообразных задач. Поэтому основную информацию по теории школьники получают от преподавателя. Но всегда могут возникнуть непредвиденные ситуации, например, ребенок заболел или не понял объяснения, даже просто отвлекся. Необходимо тщательно разобрать все упущенное, чтобы не потеряться потом в водовороте новых данных. Отличным помощником в этом деле станет <strong>сборник ответов по геометрии к учебнику Мерзляка за 7 класс</strong>. </p> <p> Подростки все чаще отдают предпочтение этому сборнику, так как: <ol> <li>в нем все понятно изложено;</li> <li>с его помощью выполнение домашних заданий отнимает всего несколько минут;</li> <li>можно исправить недочеты, до того как учитель увидит тетрадь;</li> <li>есть понятные наглядные примеры и подробные ответы, позволяющие сразу разобраться в сути вопроса.</li> </ol> <p> Заниматься с решебником можно в любое удобное время, так что учащиеся сами строят график работы, не зависят при этом от внешних условий. При этом есть постоянная возможность повторить ранее пройденные параграфы, что позволит хорошо подготовиться к контрольным и освежить память. Некоторые ребята заглядывают в пособие прямо на перемене, чем обеспечивают себе твердую пятерку на уроке. </p> <h2> Действительно ли онлайн-решебник помогает? </h2> <p> Многие взрослые беспокоятся, правда ли <strong>онлайн ответы по геометрии 7 класс к учебнику Мерзляка А. Г. (Вентана-Граф)</strong>» могут помочь детям или это просто очередная шпаргалка, которой они пользуются, лишь бы не учиться? Все зависит от подхода самих школьников. Естественно, есть ребята, которые начинают списывать с электронного пособия готовые решения. Правда, пользы это приносит мало, ведь учитель после первой же контрольной заметит, что ученик ничего не знает. </p> <p> Большинство же подростков: <ul> <li>изучают теорию в учебнике (если, конечно, она присутствует);</li> <li>самостоятельно выполняют домашнее задание;</li> <li>сверяют получившиеся ответы с теми, что даны в решебнике;</li> <li>у кого есть ошибки проводят их разбор и анализ.</li> </ul> <p> Учащиеся, которые подходят к использованию справочника ответственно, быстро добиваются хороших результатов, выбиваются в отличники и всегда уверены в том, что справятся с любыми поставленными задачами. </p>" "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 904 "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 {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1037} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1039} "field_author" => Illuminate\Database\Eloquent\Collection {#1042} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1046} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_country" => Illuminate\Database\Eloquent\Collection {#1049} "field_city" => Illuminate\Database\Eloquent\Collection {#1051} "field_series" => Illuminate\Database\Eloquent\Collection {#1053} "field_umk" => Illuminate\Database\Eloquent\Collection {#1054} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1055} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1056} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1059} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1060} "field_under_the_edition_degree" => null "field_cover_description" => "с графиком" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1017" "field_priority" => "6" "field_default_folder" => "/geometrija_07/merzlyak-u23/" "field_isbn" => "978-5-09-105805-5" "field_cover" => array:1 [ 0 => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" "alt" => "" "width" => "2277" "height" => "3035" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1062} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1063} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1064} "field_url" => "/7-klass/geometrija/merzlyak-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1065} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2>Нужно ли изучать геометрию? </h2> <p> В седьмом классе учебные нагрузки возрастут. В расписании школьников появится такой предмет как геометрия. Поначалу новая наука вызывает искренний интерес, но уже через некоторое время ребята начинают испытывать трудности при ее освоении. Многие пытаются мотивировать нежелание делать уроки высказываниями вроде: «Да зачем она нужна?», «В жизни такое точно не пригодится», и т.д. Тем не менее оценки по предмету самым прямым образом влияют на общую успеваемость. С помощью «<strong>ГДЗ по Геометрии 7 класс Учебник Мерзляк, Полонский, Якир (Вентана-Граф)</strong>» можно разобраться в аспектах дисциплины и осознать ее смысл. </p> <p> Давайте рассмотрим, какие качества позволяет развить геометрия у учеников: <ol> <li>Логическое, образное мышление.</li> <li>Пространственное представление.</li> <li>Интуитивную и символическую умственную деятельность.</li> <li>Фантазию.</li> <li>Умение анализировать.</li> <li>Грамотную речь.</li> </ol> <p> Основное, что требуется от учащихся на уроках - внимательность. Иначе будет трудно понять, каким образом знание теорем поможет справиться с выполнением задач. Геометрия - наука сугубо практическая, поэтому учителя показывают наглядные примеры во время занятий. Но иногда у подростков все равно остаются вопросы, ответить на которые зачастую некому. Решебник позволит полноценно освоить новую тему и приобрести важные навыки. </p> <h2> Почему ученики выбирают ГДЗ к учебнику Мерзляка? </h2> <p> Учебники подчас содержат очень мало полезных сведений. Возникает ощущение, что авторы этих пособий сосредоточены только на написании разнообразных задач. Поэтому основную информацию по теории школьники получают от преподавателя. Но всегда могут возникнуть непредвиденные ситуации, например, ребенок заболел или не понял объяснения, даже просто отвлекся. Необходимо тщательно разобрать все упущенное, чтобы не потеряться потом в водовороте новых данных. Отличным помощником в этом деле станет <strong>сборник ответов по геометрии к учебнику Мерзляка за 7 класс</strong>. </p> <p> Подростки все чаще отдают предпочтение этому сборнику, так как: <ol> <li>в нем все понятно изложено;</li> <li>с его помощью выполнение домашних заданий отнимает всего несколько минут;</li> <li>можно исправить недочеты, до того как учитель увидит тетрадь;</li> <li>есть понятные наглядные примеры и подробные ответы, позволяющие сразу разобраться в сути вопроса.</li> </ol> <p> Заниматься с решебником можно в любое удобное время, так что учащиеся сами строят график работы, не зависят при этом от внешних условий. При этом есть постоянная возможность повторить ранее пройденные параграфы, что позволит хорошо подготовиться к контрольным и освежить память. Некоторые ребята заглядывают в пособие прямо на перемене, чем обеспечивают себе твердую пятерку на уроке. </p> <h2> Действительно ли онлайн-решебник помогает? </h2> <p> Многие взрослые беспокоятся, правда ли <strong>онлайн ответы по геометрии 7 класс к учебнику Мерзляка А. Г. (Вентана-Граф)</strong>» могут помочь детям или это просто очередная шпаргалка, которой они пользуются, лишь бы не учиться? Все зависит от подхода самих школьников. Естественно, есть ребята, которые начинают списывать с электронного пособия готовые решения. Правда, пользы это приносит мало, ведь учитель после первой же контрольной заметит, что ученик ничего не знает. </p> <p> Большинство же подростков: <ul> <li>изучают теорию в учебнике (если, конечно, она присутствует);</li> <li>самостоятельно выполняют домашнее задание;</li> <li>сверяют получившиеся ответы с теми, что даны в решебнике;</li> <li>у кого есть ошибки проводят их разбор и анализ.</li> </ul> <p> Учащиеся, которые подходят к использованию справочника ответственно, быстро добиваются хороших результатов, выбиваются в отличники и всегда уверены в том, что справятся с любыми поставленными задачами. </p>" "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" => 599548 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Окружность и круг. 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=> "22" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_page_start" => "154" "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 {#1084 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1085 …2} ] #original: array:24 [ "id" => 599555 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Описанная и вписанная окружности треугольника" "field_branch_order" => "22" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_page_start" => "154" "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 {#1084 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1085 …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" => 599557 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1079} "field_page_start" => "157" "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 {#1080} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #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 {#1086 #items: array:7 [ 0 => App\Models\Element {#1087 #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" => 744706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Edition {#1089 #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" => 1662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие 2023" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 …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" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие 2023" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 …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" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1094 …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" => "600361" "type" => "task" ] "text" => "<p><strong>614.</strong> На каком из рисунков 348, а, б, в, изображена окружность, описанная около треугольника?</p><p>Рис. 348</p><p><strong>а</strong></p><p><strong>б</strong></p><p><strong>в</strong></p>" "img" => array:1 [ 0 => array:5 [ "name" => "614-1.jpg" "alt" => null "width" => "1705" "height" => 741 "path" => "/media/geometrija_07/merzlyak-u23/0-00/614-1.webp?ts=1738080597" ] ] ] #original: array:7 [ "id" => 744706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1088} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "text" => "<p><strong>614.</strong> На каком из рисунков 348, а, б, в, изображена окружность, описанная около треугольника?</p><p>Рис. 348</p><p><strong>а</strong></p><p><strong>б</strong></p><p><strong>в</strong></p>" "img" => array:1 [ 0 => array:5 [ "name" => "614-1.jpg" "alt" => null "width" => "1705" "height" => 741 "path" => "/media/geometrija_07/merzlyak-u23/0-00/614-1.webp?ts=1738080597" ] ] ] #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 {#1095 #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" => 1441767 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Edition {#1097 #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" => 5355 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 6 (2023)" "field_order" => "7" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1098 …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" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "6-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5355 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 6 (2023)" "field_order" => "7" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1098 …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" => "vadim" "field_edition_type" => "solution" "field_root_dir" => "6-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1102 …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" => "600361" "type" => "task" ] "text" => "<p>Окружность называется <strong>описанной около треугольника</strong>, если она проходит через все три его вершины. Треугольник при этом называется вписанным в окружность. Рассмотрим каждый из предложенных рисунков, чтобы определить, какой из них соответствует этому определению.</p><p><strong>а)</strong> На этом рисунке треугольник находится внутри окружности, но его вершины не лежат на самой окружности. Таким образом, окружность не проходит через все вершины треугольника, а значит, не является описанной.</p><p><strong>б)</strong> На данном рисунке мы видим, что все три вершины треугольника расположены точно на окружности. Это полностью соответствует определению окружности, описанной около треугольника.</p><p><strong>в)</strong> На этом рисунке окружность касается всех трех сторон треугольника изнутри. Такая окружность называется <strong>вписанной</strong> в треугольник, а не описанной около него.</p><p>Следовательно, единственным рисунком, на котором изображена окружность, описанная около треугольника, является рисунок б.</p><p>Ответ: б.</p>" ] #original: array:6 [ "id" => 1441767 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "text" => "<p>Окружность называется <strong>описанной около треугольника</strong>, если она проходит через все три его вершины. Треугольник при этом называется вписанным в окружность. Рассмотрим каждый из предложенных рисунков, чтобы определить, какой из них соответствует этому определению.</p><p><strong>а)</strong> На этом рисунке треугольник находится внутри окружности, но его вершины не лежат на самой окружности. Таким образом, окружность не проходит через все вершины треугольника, а значит, не является описанной.</p><p><strong>б)</strong> На данном рисунке мы видим, что все три вершины треугольника расположены точно на окружности. Это полностью соответствует определению окружности, описанной около треугольника.</p><p><strong>в)</strong> На этом рисунке окружность касается всех трех сторон треугольника изнутри. Такая окружность называется <strong>вписанной</strong> в треугольник, а не описанной около него.</p><p>Следовательно, единственным рисунком, на котором изображена окружность, описанная около треугольника, является рисунок б.</p><p>Ответ: б.</p>" ] #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 {#1103 #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" => 748289 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Edition {#1105 #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" => 1668 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие (2015-2022)" "field_order" => "8" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106 …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" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "old0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1110 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1668 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие (2015-2022)" "field_order" => "8" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106 …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" => "margarita" "field_edition_type" => "statement" "field_root_dir" => "old0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1110 …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" => "600361" "type" => "task" ] "text" => "<p><strong>614.</strong> Постройте треугольник по стороне и проведённым к этой стороне высоте и медиане.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "614-1.jpg" "alt" => null "width" => "1621" "height" => 174 "path" => "/media/geometrija_07/merzlyak-u23/old0-00/614-1.webp?ts=1738081593" ] ] ] #original: array:7 [ "id" => 748289 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "text" => "<p><strong>614.</strong> Постройте треугольник по стороне и проведённым к этой стороне высоте и медиане.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "614-1.jpg" "alt" => null "width" => "1621" "height" => 174 "path" => "/media/geometrija_07/merzlyak-u23/old0-00/614-1.webp?ts=1738081593" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Element {#1111 #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" => 752045 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ 0 => App\Models\Edition {#1113 #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" => 1669 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (2015-2022)" "field_order" => "9" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "margarita" "field_edition_type" => "solution" "field_root_dir" => "old2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1669 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (2015-2022)" "field_order" => "9" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "margarita" "field_edition_type" => "solution" "field_root_dir" => "old2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1118 …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" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.png" "alt" => null "width" => "694" "height" => 5402 "path" => "/media/geometrija_07/merzlyak-u23/old2-00/614-1.webp?ts=1738089319" ] ] ] #original: array:6 [ "id" => 752045 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.png" "alt" => null "width" => "694" "height" => 5402 "path" => "/media/geometrija_07/merzlyak-u23/old2-00/614-1.webp?ts=1738089319" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Element {#1119 #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" => 753407 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Edition {#1121 #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" => 1670 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3 (2015-2022)" "field_order" => "10" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "margarita" "field_edition_type" => "solution" "field_root_dir" => "old3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1670 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 3 (2015-2022)" "field_order" => "10" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "margarita" "field_edition_type" => "solution" "field_root_dir" => "old3-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1126 …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" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.png" "alt" => null "width" => "1400" "height" => 2242 "path" => "/media/geometrija_07/merzlyak-u23/old3-00/614-1.webp?ts=1738091803" ] ] ] #original: array:6 [ "id" => 753407 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1120} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.png" "alt" => null "width" => "1400" "height" => 2242 "path" => "/media/geometrija_07/merzlyak-u23/old3-00/614-1.webp?ts=1738091803" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Element {#1127 #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" => 754337 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Edition {#1129 #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" => 1671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4 (2015-2022)" "field_order" => "11" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "margarita" "field_edition_type" => "solution" "field_root_dir" => "old4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_content_source" => null ] #original: array:21 [ "id" => 1671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 4 (2015-2022)" "field_order" => "11" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "margarita" "field_edition_type" => "solution" "field_root_dir" => "old4-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1132 …2} …5 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.jpg" "alt" => null "width" => "600" "height" => 321 "path" => "/media/geometrija_07/merzlyak-u23/old4-00/614-1.webp?ts=1738092776" ] ] ] #original: array:6 [ "id" => 754337 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.jpg" "alt" => null "width" => "600" "height" => 321 "path" => "/media/geometrija_07/merzlyak-u23/old4-00/614-1.webp?ts=1738092776" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Element {#1135 #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" => 754985 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Edition {#1137 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.png" "alt" => null "width" => "777" "height" => 1609 "path" => "/media/geometrija_07/merzlyak-u23/old5-00/614-1.webp?ts=1738093186" ] ] ] #original: array:6 [ "id" => 754985 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1136} "task" => array:2 [ "refs" => "600361" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "614-1.png" "alt" => null "width" => "777" "height" => 1609 "path" => "/media/geometrija_07/merzlyak-u23/old5-00/614-1.webp?ts=1738093186" ] ] ] #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" => "600362" "type" => "task" ] "previous" => array:2 [ "refs" => "600360" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1158 #items: array:1 [ 0 => App\Models\BookPage {#1157 #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" => 964982 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "158" "field_url" => "/7-klass/geometrija/merzlyak-fgos/page-158" "field_display_title" => "158" "field_folder" => "1" "field_image_name" => "158" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1159 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:1 [ 0 => App\Models\Book {#1160 #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 [ …50] #original: array:50 [ …50] #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 {#1194 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:2 [ 0 => App\Models\Element {#1206 #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] } 1 => App\Models\Element {#1213 #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" => "964983" "type" => "book_page" ] "previous" => array:2 [ "refs" => "964981" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1790 #items: array:4 [ 0 => App\Models\Task {#1203 #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 {#1366 #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 {#1518 #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 {#1670 #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" => 964982 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "158" "field_url" => "/7-klass/geometrija/merzlyak-fgos/page-158" "field_display_title" => "158" "field_folder" => "1" "field_image_name" => "158" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1159} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1196} "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 {#1194} "content" => Illuminate\Database\Eloquent\Collection {#1197} "next" => array:2 [ "refs" => "964983" "type" => "book_page" ] "previous" => array:2 [ "refs" => "964981" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1790} ] #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" => 600361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "158" "field_page_end" => null "field_url" => "/7-klass/geometrija/merzlyak-fgos/614" "field_display_title" => "614" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "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 {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1068} "content" => Illuminate\Database\Eloquent\Collection {#1086} "next" => array:2 [ "refs" => "600362" "type" => "task" ] "previous" => array:2 [ "refs" => "600360" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1143} "page" => array:2 [ "refs" => "964982" "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 => "*" ] }
№614 (с. 158)
Условие 2023. №614 (с. 158)
скриншот условия
614. На каком из рисунков 348, а, б, в, изображена окружность, описанная около треугольника?
Рис. 348
а
б
в
Решение 6 (2023). №614 (с. 158)
Окружность называется описанной около треугольника, если она проходит через все три его вершины. Треугольник при этом называется вписанным в окружность. Рассмотрим каждый из предложенных рисунков, чтобы определить, какой из них соответствует этому определению.
а) На этом рисунке треугольник находится внутри окружности, но его вершины не лежат на самой окружности. Таким образом, окружность не проходит через все вершины треугольника, а значит, не является описанной.
б) На данном рисунке мы видим, что все три вершины треугольника расположены точно на окружности. Это полностью соответствует определению окружности, описанной около треугольника.
в) На этом рисунке окружность касается всех трех сторон треугольника изнутри. Такая окружность называется вписанной в треугольник, а не описанной около него.
Следовательно, единственным рисунком, на котором изображена окружность, описанная около треугольника, является рисунок б.
Ответ: б.
Условие (2015-2022). №614 (с. 158)
скриншот условия
614. Постройте треугольник по стороне и проведённым к этой стороне высоте и медиане.
Решение 2 (2015-2022). №614 (с. 158)
Решение 3 (2015-2022). №614 (с. 158)
Решение 4 (2015-2022). №614 (с. 158)
Решение 5 (2015-2022). №614 (с. 158)
Другие задания:
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