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Sum of distances

Source: Sharygin Geometry Olympiad 2012 - Problem 12

April 28, 2012
geometrycircumcircleincentergeometry unsolved

Problem Statement

Let OO be the circumcenter of an acute-angled triangle ABCABC. A line passing through OO and parallel to BCBC meets ABAB and ACAC in points PP and QQ respectively. The sum of distances from OO to ABAB and ACAC is equal to OAOA. Prove that PB+QC=PQPB + QC = PQ.
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