# Rinse and repeat ....

Geometry Level 5

Suppose a cyclical quadrilateral $$ABCD$$ is such that

(i) $$AB = AD = 1$$,

(ii) $$CD = \cos(\angle ABC)$$ and

(iii) $$\cos(\angle BAD) = -\dfrac{1}{3}.$$

The ratio of the area of $$ABCD$$ to the area of the circle in which it is inscribed can be expressed as $$\dfrac{a\sqrt{b}}{c\pi}$$, where $$a,c$$ are positive coprime integers and $$b$$ is a positive square-free integer.

Find $$a + b + c$$.

×