2018 AIME I Problem 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}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.