MathDB

18

Part of 1997 IMO Shortlist

Problems(1)

Circumcircle of triangle PQR passes through midpoint of BC

Source: IMO Shortlist 1997, Q18

8/10/2008
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.
geometrycircumcircletrigonometryIMO ShortlistTriangleeasy geometry