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another way to construct Fermat point

Source: 2022 Viet Nam math olympiad for high school students D1 P2

March 20, 2023
geometry

Problem Statement

Let ABCABC be a triangle with ∠A,∠B,∠C<120∘\angle A,\angle B,\angle C <120^{\circ}, TT is its Fermat-Torricelli point. Construct 3 equilateral triangles BCD,CAE,ABFBCD, CAE, ABF outside △ABC\triangle ABC
Prove that: AD,BE,CFAD, BE, CF are concurrent at TT.
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