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China Mathematics Olympiads (National Round) 2007 Problem 4

Source:

November 28, 2010
geometrycircumcircleincentertrigonometrypower of a pointradical axisgeometry unsolved

Problem Statement

Let O,IO, I be the circumcenter and incenter of triangle ABCABC. The incircle of △ABC\triangle ABC touches BC,CA,ABBC, CA, AB at points D,E,FD, E, F repsectively. FDFD meets CACA at PP, EDED meets ABAB at QQ. MM and NN are midpoints of PEPE and QFQF respectively. Show that OI⊥MNOI \perp MN.
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