# A Cyclic Trapezoid

Geometry Level 4

$$ABCD$$ is a trapezoid with bases $$AB=5$$ and $$CD=3$$. Furthermore, $$ABCD$$ is inscribed in a circle with radius $$r$$, such that the legs $$BC$$ and $$AD$$ satisfy $$BC=AD=r$$. If $$r=\sqrt{\dfrac{a}{b}}$$, find $$a+b$$.

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