In an acute triangle ABC, points D,E,F are the feet of the altitudes from A,B,C, respectively. A line through D parallel to EF meets AC at Q and AB at R. Lines BC and EF intersect at P. Prove that the circumcircle of triangle PQR passes through the midpoint of BC.
Problem
Source: Iran Third Round MO 1997, Exam 3, P2
Tags: geometry, circumcircle, geometry proposed