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concyclic wanted, altitudes related

Source: 2013 Saudi Arabia IMO TST II p2

July 23, 2020
geometryConcyclicaltitudes

Problem Statement

Let ABCABC be an acute triangle, and let AA1,BB1AA_1, BB_1, and CC1CC_1 be its altitudes. Segments AA1AA_1 and B1C1B_1C_1 meet at point KK. The perpendicular bisector of segment A1KA_1K intersects sides ABAB and ACAC at LL and MM, respectively. Prove that points A,A1,LA,A_1, L, and MM lie on a circle.
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