Problem

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Tags: geometry, circumcircle, trigonometry, perpendicular bisector, angle bisector, geometry proposed



Let AL and BK be angle bisectors in the non-isosceles triangle ABC (L lies on the side BC, K lies on the side AC). The perpendicular bisector of BK intersects the line AL at point M. Point N lies on the line BK such that LN is parallel to MK. Prove that LN=NA.