The altitudes from A, B, C of a non-isosceles, acute-angled triangle meet the opposite sides at D, E, F respectively. The line through D parallel to EF meets CA, AB at Q, R respectively, and EF meets BC at P. Prove that the circumcircle of triangle PQR passes through the midpoint of BC.
This is Q7 from this month’s Advanced Mentoring, and the most beautiful geometry I’ve ever seen on the AMS. EVERYTHING IS CIRCLES! This means you can use power of a point over, and over, and over…











