TST TAJIKISTAN Day 2 Problem 3
Source:
July 10, 2018
TajikistanIMO TST 2018
Problem Statement
Problem 6. Let H be orthocenter of an acute-angled triangle ABC. Points E,F are on the segments AB,AC respectively, such that BE=BH,CF=CH. The lines EH,FH meet BC in X,Y respectively. Draw the perpendicular HZ from H to EF. Prove that the circumcircle of triangle XYZ is tangent to the circle with diameter BC.