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perpendicularity wanted, heights, midpoints, circumcenter related

Source: 2013 Oral Moscow Geometry Olympiad grades 10-11 p5

August 17, 2019
geometryperpendicularCircumcenter

Problem Statement

In the acute-angled triangle ABCABC, let APAP and BQBQ be the altitudes, CMCM be the median . Point RR is the midpoint of CMCM. Line PQPQ intersects line ABAB at TT. Prove that OR⊥TCOR \perp TC, where OO is the center of the circumscribed circle of triangle ABCABC.
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