Предмет: Геометрия, автор: kirilobondarenko962

Допоможіть БУТЬ ЛАСКааааааааааааавваав 9. Точка дотику кола, вписаного у прямокутну трапецію, ділить більшу бічну сторону на відрізки 2 см і 8 см. Знай- діть площу трапеції. Даю 30

Ответы

Автор ответа: dobra888
1

Відповідь:      S трап = 72 см² .

Пояснення:

   У трапеції  ABCD   BC║AD ,  BA⊥AD ; т. О - центр вписаного в

   трапецію кола . Точка М - точка дотику ; СМ = 2 см , МD = 8 см .

   ОМ = r - радіус впис. кола .  ΔOCD - прямокутний  , тому

   ОМ = r = √( CM * MD ) = √( 2 * 8 ) = √16 = 4 ( см ) ;   r = 4 см .

   За власт. дотичних , проведених із точки до кола маємо :

   h = 2 * r = 2 * 4 = 8 ( см ) .  BC = BN + CN = 4 + 2 = 6 ( см ) ;

   AD = r + MD = 4 + 8 = 12 ( см ) .

    S трап = ( BC + AD ) * h/2 = ( 6 + 12 ) * 8/2 = 18 * 4 = 72 ( см² ) ;

    S трап = 72 см² .

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