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khrustkhrustal
@khrustkhrustal
July 2022
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Найдите площадь четырёхугольника ABCD, если AB = BC = 8, AD = DC = 6 и ровно
три вершины A, B и C лежат на окружности радиуса 5.
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Alexandr130398
Sabcd=SΔabc+ SΔadc
ac=2R=2*5=10
О-центр окружности, DO-высота Δadc
DO=√(6²-5²)=√36-25=√11
SΔadc=ah/2=10*√11/2=5√11
BO-высота Δ abc
BO=√(8²-5²)=√39
SΔabc=10*√39/2=5√39
Sabcd=5√11+5√39=5(√11+√39)
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Answers & Comments
ac=2R=2*5=10
О-центр окружности, DO-высота Δadc
DO=√(6²-5²)=√36-25=√11
SΔadc=ah/2=10*√11/2=5√11
BO-высота Δ abc
BO=√(8²-5²)=√39
SΔabc=10*√39/2=5√39
Sabcd=5√11+5√39=5(√11+√39)