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proving PL=PN

Source: Turkish NMO 1996, 4. Problem

July 31, 2011
geometry proposedgeometry

Problem Statement

A circle is tangent to sides AD, DC, CBAD,\text{ }DC,\text{ }CB of a convex quadrilateral ABCDABCD at K, L, M\text{K},\text{ L},\text{ M} respectively. A line ll, passing through LL and parallel to ADAD, meets KMKM at NN and KCKC at PP. Prove that PL=PNPL=PN.
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