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<AA_1K=<BB_1M wanted, B_1K// BC, A_1M// AC, altitudes AA_1,BB_1

Source: 2009 Oral Moscow Geometry Olympiad grades 8-9 p3

September 19, 2020
geometryequal anglesparallelatltitudes

Problem Statement

In the triangle ABCABC, AA1AA_1 and BB1BB_1 are altitudes. On the side ABAB , points MM and KK are selected so that B1K∥BCB_1K \parallel BC and A1M∥ACA_1M \parallel AC. Prove that the angle AA1KAA_1K is equal to the angle BB1MBB_1M.
(D. Prokopenko)
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