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median bisects B_1C_1, projections of vertices on angle bisectors

Source: 2015 Latvia BW TST P6

December 16, 2022
geometrybisects segmentangle bisector

Problem Statement

AMAM is the median of triangle ABCABC. A perpendicular CC1CC_1 is drawn from point CC on the bisector of angle ∠CMA\angle CMA, a perpendicular BB1BB_1 is drawn from point BB on the bisector of angle ∠BMA\angle BMA. Prove that line AMAM intersects segment B1C1B_1C_1 at its midpoint.
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