TST 2018 TAJIKISTAN Day 1 Problem 1
Source:
July 10, 2018
TajikistanIMO TST 2018
Problem Statement
Problem 1. Let ω be the incircle of triangle ABC which is tangent to BC,CA,AB at points D,E,F, respectively. The altitudes of triangle DEF with respect to E,F meet AB,AC at points X,Y, respectively. Prove that the second intersection of the circumcircles of triangles AEX,AFY lies on the circle ω.