# Loving the Circles

Geometry Level 3

Two circles having radii $$r_1$$ and $$r_2$$ passing through vertex $$A$$ of a triangle $$ABC$$. One of the circle touches the side $$BC$$ at $$B$$ and other circle touches the side $$BC$$ at $$C$$. If $$a = 5$$ and $$\angle BAC = 30^\circ$$, find $$\sqrt{r_1 r_2}$$.

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