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An interesting triangle center (?) or not

Source: Sharygin Correspondence Round 2024 P18

March 6, 2024
geometry

Problem Statement

Let AA1,BB1,CC1AA_1, BB_1, CC_1 be the altitudes of an acute-angled triangle ABCABC; IaI_a be its excenter corresponding to AA; Ia′I_a' be the reflection of IaI_a about the line AA1AA_1. Points Ib′,Ic′I_b', I_c' are defined similarily. Prove that lines A1Ia′,B1Ib′,C1Ic′A_1I_a', B_1I_b', C_1I_c' concur.
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