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concurrency wanted, touchpoints with incircle, altitudes related

Source: 2022 Sharygin CR p4

March 6, 2022
geometryconcurrencyconcurrent

Problem Statement

Let AA1AA_1, BB1BB_1, CC1CC_1 be the altitudes of acute angled triangle ABCABC. A2A_2 be the touching point of the incircle of triangle AB1C1AB_1C_1 with B1C1B_1C_1, points B2B_2, C2C_2 be defined similarly. Prove that the lines A1A2A_1A_2, B1B2B_1B_2, C1C2C_1C_2 concur.
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