MathDB
Equality with Fermat Point

Source: 2012 Baltic Way, Problem 11

November 22, 2012

Problem Statement

Let ABCABC be a triangle with ∠A=60∘\angle A = 60^\circ. The point TT lies inside the triangle in such a way that ∠ATB=∠BTC=∠CTA=120∘\angle ATB = \angle BTC = \angle CTA = 120^\circ. Let MM be the midpoint of BCBC. Prove that TA+TB+TC=2AMTA + TB + TC = 2AM.
Back to ProblemsView on AoPS