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Part of 2011 Costa Rica - Final Round

Problems(1)

Orthocenter is incenter of triangle

Source: Costa Rica National Olympiad, Final Round, Problem 1

11/26/2011
Let ABCABC be a triangle with orthocenter HH. Let P,Q,RP,Q,R be the reflections of HH with respect to sides BC,AC,ABBC,AC,AB, respectively. Show that HH is incenter of PQRPQR.
geometryincentergeometric transformationreflectioncircumcircledilationsymmetry