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medians AN _|_ CM, when BC=\sqrt2 AC, right triangle (2019 Kyiv City MO 9.2)

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September 16, 2020
geometryMediansperpendicular

Problem Statement

In a right triangle ABCABC, the lengths of the legs satisfy the condition: BC=2ACBC =\sqrt2 AC. Prove that the medians ANAN and CMCM are perpendicular.
(Hilko Danilo)
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