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collinearity

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March 6, 2015
geometry unsolvedgeometry

Problem Statement

Given a non-isosceles triangle ABCABC with incircle kk with center SS. kk touches the side BC,CA,ABBC,CA,AB at P,Q,RP,Q,R respectively. The line QRQR and line BCBC intersect at MM. A circle which passes through BB and CC touches kk at NN. The circumcircle of triangle MNPMNP intersects APAP at LL. Prove that S,L,MS,L,M are collinear.
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