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ASU 084 All Soviet Union MO 1967 height AH=BM median

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June 20, 2019
geometryaltitudemedianEquilateral

Problem Statement

a) The maximal height ∣AH∣|AH| of the acute-angled triangle ABCABC equals the median ∣BM∣|BM|. Prove that the angle ABCABC isn't greater than 6060 degrees.
b) The height ∣AH∣|AH| of the acute-angled triangle ABCABC equals the median ∣BM∣|BM| and bisectrix ∣CD∣|CD|. Prove that the angle ABCABC is equilateral.
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