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angle wanted, <ACB=75^o, altitudes, parallels, circumcircle

Source: December 2020 Ukraine Geometry Olympiad XI p5

December 20, 2020
geometryanglesaltitudescircumcircle

Problem Statement

In an acute triangle ABCABC with an angle ∠ACB=75o\angle ACB =75^o, altitudes AA3,BB3AA_3,BB_3 intersect the circumscribed circle at points A1,B1A_1,B_1 respectively. On the lines BCBC and CACA select points A2A_2 and B2B_2 respectively suchthat the line B1B2B_1B_2 is parallel to the line BCBC and the line A1A2A_1A_2 is parallel to the line ACAC . Let MM be the midpoint of the segment A2B2A_2B_2. Find in degrees the measure of the angle ∠B3MA3\angle B_3MA_3.
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