Question 13
Let $\triangle ABC$ have side lengths $AB = 30,$ $BC = 32,$ and $AC = 34.$ Point $X$ lies in the interior of $\overline{BC},$ and points $I_1$ and $I_2$ are the incenters of $\triangle ABX$ and $\triangle ACX,$ respectively. Find the minimum possible area of $\triangle AI_1I_2$ as $X$ varies along $\overline{BC}.$