MathDB
Bisecting Segment

Source: 2020 Taiwan TST Round 1 Independent Study 2-2

May 23, 2020
geometrycircumcircle

Problem Statement

Let point HH be the orthocenter of a scalene triangle ABCABC. Line AHAH intersects with the circumcircle Ω\Omega of triangle ABCABC again at point PP. Line BH,CHBH, CH meets with AC,ABAC,AB at point EE and FF, respectively. Let PE,PFPE, PF meet Ω\Omega again at point Q,RQ,R, respectively. Point YY lies on Ω\Omega so that lines AY,QRAY,QR and EFEF are concurrent. Prove that PYPY bisects EFEF.
Back to ProblemsView on AoPS