MathDB
perpendicularity wanted, <PAC = <QAB, <PBC = <QBA given

Source: 2012 Balkan Shortlist G6 BMO

April 3, 2020
perpendicularequal anglesgeometry

Problem Statement

Let PP and QQ be points inside a triangle ABCABC such that ∠PAC=∠QAB\angle PAC = \angle QAB and ∠PBC=∠QBA\angle PBC = \angle QBA. Let DD and EE be the feet of the perpendiculars from PP to the lines BCBC and ACAC, and FF be the foot of perpendicular from QQ to the line ABAB. Let MM be intersection of the lines DEDE and ABAB. Prove that MP⊥CFMP \perp CF
Back to ProblemsView on AoPS