MathDB

6

Part of 2015 Latvia Baltic Way TST

Problems(1)

median bisects B_1C_1, projections of vertices on angle bisectors

Source: 2015 Latvia BW TST P6

12/16/2022
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.
geometrybisects segmentangle bisector