MathDB
perpendicular medians (old exercise)

Source: Ireland 2001

July 5, 2009
geometry proposedgeometry

Problem Statement

Let ABC ABC be a triangle with sides BC\equal{}a, CA\equal{}b,AB\equal{}c and let D D and E E be the midpoints of AC AC and AB AB, respectively. Prove that the medians BD BD and CE CE are perpendicular to each other if and only if b^2\plus{}c^2\equal{}5a^2.
Back to ProblemsView on AoPS