In $\triangle ABC$, $\angle A = 30^{\circ}$, $BC = 13$. Given two circles $\gamma_1$ and $\gamma_2$ with radii $r_1$ and $r_2$, respectively, contain point $A$ and touch line $BC$ at points $B$ and $C$. Find the product $r_1r_2$.

Let's think step by step and output the final answer within \boxed{}.
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