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Projection to bisector

Source: Sharygin Geometry Olympiad 2012 - Problem 4

April 28, 2012
analytic geometrygeometryparallelogramratioperpendicular bisectorcongruent trianglesgeometry unsolved

Problem Statement

Given triangle ABCABC. Point MM is the midpoint of side BCBC, and point PP is the projection of BB to the perpendicular bisector of segment ACAC. Line PMPM meets ABAB in point QQ. Prove that triangle QPBQPB is isosceles.
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