2011 AIME I Problem 4

In triangle ABC, AB = 125, AC = 117, and BC = 120. The angle bisector of angle A intersects \overline{BC} at point L, and the angle bisector of angle B intersects \overline{AC} at point K. Let M and N be the feet of the perpendiculars from C to \overline{BK} and \overline{AL}, respectively. Find MN.

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.