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Консультация № 189675
10.08.2016, 11:04
0.00 руб.
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Здравствуйте! У меня возникли сложности с такой задачей:
Прикрепленные файлы:
Обсуждение
11.08.2016, 11:03
общий
это ответ
Здравствуйте, anton74551!
Середины диагоналей лежат на серединах высот трапеции, поэтому PQ||AD||BC
отсюда следует и подобие треугольников [$8895$]AOD, [$8895$]POQ и [$8895$]BOC
Учитывая, что P - середина AC
OP=OA-(1/2)(OA+OC)
при этом, из подобия треугольников следует
PQ/OP=AD/OA=BC/OC
что даёт нам
PQ=AD-(1/2)(AD+BC)=a-(a+b)/2=(a-b)/2
Гипотенуза прямоугольного треугольника является диаметром описанной окружности, поэтому опущенная на гипотенузу медиана равна половине гипотенузы.
OM=AD/2=a/2
ON=BC/2=b/2
MN=(a+b)/2
В итоге
MN[$183$]PQ=(a+b)(a-b)/4=(a2-b2)/4
Середины диагоналей лежат на серединах высот трапеции, поэтому PQ||AD||BC
отсюда следует и подобие треугольников [$8895$]AOD, [$8895$]POQ и [$8895$]BOC
Учитывая, что P - середина AC
OP=OA-(1/2)(OA+OC)
при этом, из подобия треугольников следует
PQ/OP=AD/OA=BC/OC
что даёт нам
PQ=AD-(1/2)(AD+BC)=a-(a+b)/2=(a-b)/2
Гипотенуза прямоугольного треугольника является диаметром описанной окружности, поэтому опущенная на гипотенузу медиана равна половине гипотенузы.
OM=AD/2=a/2
ON=BC/2=b/2
MN=(a+b)/2
В итоге
MN[$183$]PQ=(a+b)(a-b)/4=(a2-b2)/4
5
Спасибо огромное за помощь !
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