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International competition SRMC 2003 P-2

Source:

September 8, 2010
geometryperimetercircumcircleincenterEulerparallelogramtrapezoid

Problem Statement

Let s=AB+BC+AC2s=\frac{AB+BC+AC}{2} be half-perimeter of triangle ABCABC. Let LL and NNbe a point's on ray's ABAB and CBCB, for which AL=CN=sAL=CN=s. Let KK is point, symmetric of point BB by circumcenter of ABCABC. Prove, that perpendicular from KK to NLNL passes through incenter of ABCABC.
Solution for problem [url=http://www.artofproblemsolving.com/Forum/viewtopic.php?f=125&t=365714&p=2011659#p2011659]here
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