2018 AIME I Problem 13

Let \triangle A B C have side lengths A B=30, B C=32, and A C=34. Point X lies in the interior of \overline{B C}, and points I_{1} and I_{2} are the incenters of \triangle A B X and \triangle A C X, respectively. Find the minimum possible area of \triangle A I_{1} I_{2} as X varies along \overline{B C}.