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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