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PQ passes through the circumcenter of ABC

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August 29, 2010
geometrycircumcircleratiogeometry unsolved

Problem Statement

Let PP and QQ be distinct points in the plane of a triangle ABCABC such that AP:AQ=BP:BQ=CP:CQAP : AQ = BP : BQ = CP : CQ. Prove that the line PQPQ passes through the circumcenter of the triangle.
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