2022 AIME I Problem 14

Given \triangle ABC and a point P on one of its sides, call line \ell the \textit{splitting line} of \triangle ABC through P if \ell passes through P and divides \triangle ABC into two polygons of equal perimeter. Let \triangle ABC be a triangle where BC = 219 and AB and AC are positive integers. Let M and N be the midpoints of \overline{AB} and \overline{AC}, respectively, and suppose that the splitting lines of \triangle ABC through M and N intersect at 30^\circ. Find the perimeter of \triangle ABC.

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.