Angle biosector proof question

[EGDAVID]

AL and BK are 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.

 

[Deleted member 4993]

AL and BK are 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.

I would start with a sketch of ABC and locate points L, K & M according constraints described in the problem. Then think......

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