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Circumcircle of triangle PQR passes through midpoint of BC

Source: IMO Shortlist 1997, Q18

August 10, 2008
geometrycircumcircletrigonometryIMO ShortlistTriangleeasy geometry

Problem Statement

The altitudes through the vertices A,B,C A,B,C of an acute-angled triangle ABC ABC meet the opposite sides at D,E,F, D,E, F, respectively. The line through D D parallel to EF EF meets the lines AC AC and AB AB at Q Q and R, R, respectively. The line EF EF meets BC BC at P. P. Prove that the circumcircle of the triangle PQR PQR passes through the midpoint of BC. BC.
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