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JBMO 2010. Problem 3.

Source:

June 20, 2010
geometrycircumcircletrigonometryperpendicular bisectorangle bisectorgeometry proposed

Problem Statement

Let ALAL and BKBK be angle bisectors in the non-isosceles triangle ABCABC (LL lies on the side BCBC, KK lies on the side ACAC). The perpendicular bisector of BKBK intersects the line ALAL at point MM. Point NN lies on the line BKBK such that LNLN is parallel to MKMK. Prove that LN=NALN = NA.
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