MathDB
2021 Team P12

Source:

March 2, 2021
geometry

Problem Statement

Let △ABC\triangle ABC be a triangle, and let ll be the line passing through its incenter and centroid. Assume that BB and CC lie on the same side of ll, and that the distance from BB to ll is twice the distance from CC to ll. Suppose also that the length BABA is twice that of CACA. If △ABC\triangle ABC has integer side lengths and is as small as possible, what is AB2+BC2+CA2AB^2+BC^2+CA^2?
Proposed by Thomas Lam
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