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the same distances

Source: 2022 Viet Nam math olympiad for high school students D1 P6

March 20, 2023
geometryperpendicular bisector

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. Let GG be the centroid of △ABC\triangle ABC.
Prove that: the distances from GG to the perpendicular bisectors of TA,TB,TCTA, TB, TC are the same.
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