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1/2 < AC/ BC < 2 for perpendicular medians

Source: 2020 Sweden MO p2

February 16, 2021
geometrygeometric inequalityMedians

Problem Statement

The medians of the sides ACAC and BCBC in the triangle ABCABC are perpendicular to each other. Prove that 12<∣AC∣∣BC∣<2\frac12 <\frac{|AC|}{|BC|}<2.
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