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Part of 2003 Iran MO (3rd Round)

Problems(1)

DD', EE' and FF' intersect at Q

Source: Iranian National Olympiad (3rd Round) 2003

1/24/2009
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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