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<B= 30^o wanted, 2AC=AB,< A = 2<B, CL = ML (2019 Kyiv City MO 8.3)

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September 16, 2020
geometryequal anglesanglesequal segments

Problem Statement

In the triangle ABCABC it is known that 2AC=AB2AC=AB and ∠A=2∠B\angle A = 2\angle B. In this triangle draw the angle bisector ALAL, and mark point MM, the midpoint of the side ABAB. It turned out that CL=MLCL = ML. Prove that ∠B=30o\angle B= 30^o.
(Hilko Danilo)
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