circumcircle of triangle passes through segment's midpoint
Source: Czech and Slovak Match 1999 P2
October 1, 2017
Concyclicgeometry
Problem Statement
The altitudes through the vertices of an acute-angled triangle meet the opposite sides at respectively. The line through parallel to meets the lines and at and , respectively. The line meets at . Prove that the circumcircle of the triangle passes through the midpoint of .