IMO Shortlist 2013 problem G6

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Let the excircle of the triangle ABC lying opposite to A touch its side BC at the point A_1. Define the points B_1 and C_1 analogously. Suppose that the circumcentre of the triangle A_1B_1C_1 lies on the circumcircle of the triangle ABC. Prove that the triangle ABC is right-angled.
Izvor: Russia