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NK bisects BC, CM=MN, <MNB=<CBM, right triangle (Kyiv City Olympiad 2005 10.4)

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June 27, 2020
geometryright trianglebisects segmentequal segmentsequal angles

Problem Statement

In a right triangle ABCABC with a right angle ∠C\angle C , n the sides ACAC and ABAB, the points MM and NN are selected, respectively, that CM=MNCM = MN and ∠MNB=∠CBM\angle MNB = \angle CBM. Let the point KK be the projection of the point CC on the segment MBMB . Prove that the line NKNK passes through the midpoint of the segment BCBC.
(Alex Klurman)
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