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MN/AB =? 60-45-75 triangle (2022 Adygea Teachers' Geometry Olympiad p1)

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February 28, 2024
geometry

Problem Statement

In triangle ABCABC, ∠A=60o\angle A = 60^o,∠B=45o \angle B = 45^o. On the sides ACAC and BCBC points MM and NN are taken, respectively, so that the straight line MNMN cuts off a triangle similar to this one. Find the ratio of MNMN to ABAB if it is known that CM:AM=2:1CM : AM = 2:1.
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