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AK bisects BC, touchpoints of incircle related

Source: China Northern MO 2010 p6 CNMO

October 28, 2022
geometrybisects segmentincircle

Problem Statement

Let ⊙O\odot O be the inscribed circle of △ABC\vartriangle ABC, with DD, EE, NN the touchpoints with sides ABAB, ACAC, BCBC respectively. Extension of NONO intersects segment DEDE at point KK. Extension of AKAK intersects segment BCBC at point MM. Prove that MM is the midpoint of BCBC. https://cdn.artofproblemsolving.com/attachments/a/6/a503c500178551ddf9bdb1df0805ed22bc417d.png
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