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China 2010 quiz2 problem 1

Source:

September 8, 2010
geometrycircumcirclegeometric transformationreflectiongeometry unsolved

Problem Statement

Let △ABC\triangle ABC be an acute triangle with AB>ACAB>AC, let II be the center of the incircle. Let M,NM,N be the midpoint of ACAC and ABAB respectively. D,ED,E are on ACAC and ABAB respectively such that BD∥IMBD\parallel IM and CE∥INCE\parallel IN. A line through II parallel to DEDE intersects BCBC in PP. Let QQ be the projection of PP on line AIAI. Prove that QQ is on the circumcircle of △ABC\triangle ABC.
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