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Touching points geometry

Source: Sharygin geometry olympiad 2015, grade 10, Final Round, Problem 4

July 17, 2018
geometry

Problem Statement

Let AA1AA_1, BB1BB_1, CC1CC_1 be the altitudes of an acute-angled, nonisosceles triangle ABCABC, and A2A_2, B2B_2, C2C_2 be the touching points of sides BCBC, CACA, ABAB with the correspondent excircles. It is known that line B1C1B_1C_1 touches the incircle of ABCABC. Prove that A1A_1 lies on the circumcircle of A2B2C2A_2B_2C_2.
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