IMO ShortList 1998, geometry problem 5
Source: IMO ShortList 1998, geometry problem 5
October 14, 2004
geometrycircumcirclereflectionhomothetyparallelogramIMO Shortlistimo shortlist 1998
Problem Statement
Let be a triangle, its orthocenter, its circumcenter, and its circumradius. Let be the reflection of the point across the line , let be the reflection of the point across the line , and let be the reflection of the point across the line . Prove that the points , and are collinear if and only if .