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Prove this geometric inequality

Source: 2019 Jozsef Wildt International Math Competition

May 20, 2020
geometrytoricelli pointgeometric inequalityinequalities

Problem Statement

Denote TT the Toricelli point of the triangle ABCABC. Prove that AB2×BC2×CA2≥3(TA2×TB+TB2×TC+TC2×TA)(TA×TB2+TB×TC2+TC×TA2)AB^2 \times BC^2 \times CA^2 \geq 3(TA^2\times TB + TB^2 \times TC + TC^2 \times TA)(TA\times TB^2 + TB \times TC^2 + TC \times TA^2)
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