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Angle bisectors AL, BK; then LN=NA[Indian RMO 2012(b) Q5]

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December 2, 2012
geometrycircumcircleperpendicular bisectorangle bisectorgeometry proposed

Problem Statement

Let ALAL and BKBK be the angle bisectors in a non-isosceles triangle ABC,ABC, where LL lies on BCBC and KK lies on AC.AC. The perpendicular bisector of BKBK intersects the line ALAL at MM. Point NN lies on the line BKBK such that LNLN is parallel to MK.MK. Prove that LN=NA.LN=NA.
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