MathDB
Conjugate Points

Source: Iran TST 2004

January 9, 2009
geometry proposedgeometry

Problem Statement

Let M,M′ M,M' be two conjugates point in triangle ABC ABC (in the sense that \angle MAB\equal{}\angle M'AC,\dots). Let P,Q,R,P′,Q′,R′ P,Q,R,P',Q',R' be foots of perpendiculars from M M and M′ M' to BC,CA,AB BC,CA,AB. Let E\equal{}QR\cap Q'R', F\equal{}RP\cap R'P' and G\equal{}PQ\cap P'Q'. Prove that the lines AG,BF,CE AG, BF, CE are parallel.
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