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"Updating" China TST 2002

Source: Romanian TST 4 2008, Problem 1

June 13, 2008
Gaussgeometry proposedgeometry

Problem Statement

Let ABCD ABCD be a convex quadrilateral and let O∈AC∩BD O \in AC \cap BD, P∈AB∩CD P \in AB \cap CD, Q∈BC∩DA Q \in BC \cap DA. If R R is the orthogonal projection of O O on the line PQ PQ prove that the orthogonal projections of R R on the sidelines of ABCD ABCD are concyclic.
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