Let M,M′ be two conjugates point in triangle ABC (in the sense that \angle MAB\equal{}\angle M'AC,\dots). Let P,Q,R,P′,Q′,R′ be foots of perpendiculars from M and M′ to 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 are parallel. geometry proposedgeometry