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Three altitudes of a triangle. Circumscribed quadrilateral wanted

Source: St. Petersburg MO 2000, 11th grade, P5

April 22, 2023
geometryaltitudescircumscribed quadrilateral

Problem Statement

Let AA1AA_1, BB1BB_1, CC1CC_1 be the altitudes of an acute angled triangle ABCABC. On the side BCBC point KK is taken such that ∠BB1K=∠A\angle BB_1K=\angle A. On the side ABAB a point MM is taken such that ∠BB1M∠C\angle BB_1M\angle C. Let LL be the intersection of BB1BB_1 and A1C1A_1C_1. Prove that the quadrilateral B1KLMB_1KLM is circumscribed.
[I]Proposed by A. Khrabrov, D. Rostovski
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