MathDB
Circle pass through mid of bc

Source: Iran Third Round MO 1997, Exam 3, P2

October 18, 2005
geometrycircumcirclegeometry proposed

Problem Statement

In an acute triangle ABCABC, points D,E,FD,E,F are the feet of the altitudes from A,B,CA,B,C, respectively. A line through DD parallel to EFEF meets ACAC at QQ and ABAB at RR. Lines BCBC and EFEF intersect at PP. Prove that the circumcircle of triangle PQRPQR passes through the midpoint of BCBC.