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Problem 5 of Third round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018
geometry

Problem Statement

On the sides ABAB,BCBC, and CACA of △ABC\triangle ABC are chosen points C1C_1, A1A_1, and B1B_1 respectively, in such way that AA1AA_1, BB1BB_1, and CC1CC_1 intersect in one point XX. If ∠A1C1B=∠B1C1A\angle A_1C_1B = \angle B_1C_1A, prove that CC1CC_1 is perpendicular to ABAB.
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