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perpendicular wanted , where O is circumcenter

Source: Switzerland - Swiss TST 2001 p7

February 18, 2020
geometryCircumcenterperpendicular

Problem Statement

Let ABCABC be an acute-angled triangle with circumcenter OO. The circle SS through A,BA,B, and OO intersects ACAC and BCBC again at points PP and QQ respectively. Prove that CO⊥PQCO \perp PQ.
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