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midpoints of the altitudes

Source: All-Russian olympiad 1995, Grade 9, Second Day, Problem 6

October 20, 2013
geometrygeometry proposed

Problem Statement

In an acute-angled triangle ABC, points A2A_2, B2B_2, C2C_2 are the midpoints of the altitudes AA1AA_1, BB1BB_1, CC1CC_1, respectively. Compute the sum of angles B2A1C2B_2A_1C_2, C2B1A2C_2B_1A_2 and A2C1B2A_2C_1B_2. D. Tereshin
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