IMO 2013 Shortlist G6
Let the excircle of the triangle ABC lying opposite to A touch its side BC at the point A1. Define the points B1 and C1 ...
Category: Geometry
Problem
Let the excircle of the triangle ABC lying opposite to A touch its side BC at the point A1. Define the points B1 and C1 analogously. Suppose that the circumcentre of the triangle A1B1C1 lies on the circumcircle of the triangle ABC. Prove that the triangle ABC is right-angled. (Russia) Shortlisted problems 7