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isogonal mittenpunkt concurrency gets resurrected

Source: Sharygin 2023 - P6 (Grade-8-9)

March 4, 2023
geometrymittenpunktconcurrencySharygin Geometry OlympiadSharygin 2023

Problem Statement

Let A1,B1,C1A_1, B_1, C_1 be the feet of altitudes of an acute-angled triangle ABCABC. The incircle of triangle A1B1C1A_1B_1C_1 touches A1B1,A1C1,B1C1A_1B_1, A_1C_1, B_1C_1 at points C2,B2,A2C_2, B_2, A_2 respectively. Prove that the lines AA2,BB2,CC2AA_2, BB_2, CC_2 concur at a point lying on the Euler line of triangle ABCABC.
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