Предмет: Геометрия, автор: markusha16

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Автор ответа: ilanedola

Объяснение:

Пусть проведены высоты ВВ₁ и СС₁, ВС=В₁С₁=8, DC₁=АВ₁=(20-8)/2=6/см/, АС₁=6+8=14, тогда диагональ АС=√ (АС₁²+СС₁²)=(√(14²+8²)=

√260=2√65 /см/, боковые стороны равны по

√(ВВ₁²+АВ₁²)=(√(8²+6²)=10/см/

Окружность описана не только около трапеции, но и около треугольника АСD, стороны которого нам известны, найдем площадь этого треугольника АD*СС₁/2=20*8/2=80/см²/, теперь по формуле для нахождения радиуса описанной окружности найдем этот радиус.

R=a*b*c/(4S)=10*20*2√65/(4*80)=1.25√65/см/

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