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DD', EE' and FF' intersect at Q

Source: Iranian National Olympiad (3rd Round) 2003

January 24, 2009
geometrygeometry proposed

Problem Statement

Let A,B,C,Q A,B,C,Q be fixed points on plane. M,N,P M,N,P are intersection points of AQ,BQ,CQ AQ,BQ,CQ with BC,CA,AB BC,CA,AB. D′,E′,F′ D',E',F' are tangency points of incircle of ABC ABC with BC,CA,AB BC,CA,AB. Tangents drawn from M,N,P M,N,P (not triangle sides) to incircle of ABC ABC make triangle DEF DEF. Prove that DD′,EE′,FF′ DD',EE',FF' intersect at Q Q.
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