MathForces: Math Olympiads
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Author: daniyar
Problem has been solved: 50 times

Русский язык | English Language

The quadrilateral $ ABCD $ is inscribed in the unit circle with a diameter of $ AB $. It turned out that the point $ D $ lies on the bisector $ \angle CBA $ and the areas of the triangles $ ABC $ and $ CDA $ are equal. The area of the quadrilateral $ ABCD $ is representable in the form $ \frac {a \sqrt {b}} {c} $, where $ (a,b,c)=1$ and $ b $ is not divisible by a square one of the prime numbers. Find $ abc $.

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