IMO Shortlist 1982 problem 17


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The right triangles ABC and AB_1C_1 are similar and have opposite orientation. The right angles are at C and C_1, and we also have \angle CAB = \angle C_1AB_1. Let M be the point of intersection of the lines BC_1 and B_1C. Prove that if the lines AM and CC_1 exist, they are perpendicular.
Izvor: Međunarodna matematička olimpijada, shortlist 1982