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Midpoints of nagelians

Source: 239 School Open MO, 2023, Senior league, Problem 2

March 30, 2023
geometry

Problem Statement

The excircles of triangle ABCABC touch its sides BCBC, CACA, and ABAB at points A1A_1, B1B_1, and C1C_1, respectively. Let B2B_2 and C2C_2 be the midpoints of segments BB1BB_1 and CC1CC_1, respectively. Line B2C2B_2C_2 intersects line BCBC at point WW. Prove that AW=A1WAW = A_1W.
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