# Diameter

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 $abc$.