MathDB

2

Part of 2020 Swedish Mathematical Competition

Problems(1)

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

Source: 2020 Sweden MO p2

2/16/2021
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.
geometrygeometric inequalityMedians