# It will all click together

Geometry Level 5

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

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

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

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

Let $$R$$ be the radius of the circle in which $$ABCD$$ is inscribed. Find $$\lfloor 1000*R \rfloor$$.

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