MathDB
Triangle and angle bisectors

Source:

March 18, 2011
geometrygeometric transformationhomothetytrigonometryangle bisectortrig identitiesLaw of Sines

Problem Statement

In triangle ABCABC, AB=125,AC=117AB=125,AC=117, and BC=120BC=120. The angle bisector of angle AA intersects BC\overline{BC} at point LL, and the angle bisector of angle BB intersects AC\overline{AC} at point KK. Let MM and NN be the feet of the perpendiculars from CC to BK\overline{BK} and AL\overline{AL}, respectively. Find MNMN.