[This problem is worth 7 points.]
Let ABC be a triangle with AB = 125, AC = 117, and BC = 120. Let the angle bisector of A intersect BC at L, and the angle bisector of B intersect AC at K. Let M be the point of intersection of the perpendicular from C to BK, and let N be the point of intersection of the perpendicular from C to AL. Find MN.
