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inequality with Lemoine point

Source: 2023 Viet Nam math olympiad for high school students D1 P8

March 25, 2023
geometry

Problem Statement

Given a triangle ABCABC with symmedians AD,BE,CFAD,BE,CF concurrent at Lemoine point L(D,E,FL(D,E,F are on the sides BC,CA,AB,BC,CA,AB, respectively).). Prove that: LA+LB+LC≥2(LD+LE+LF).LA+LB+LC\ge 2(LD+LE+LF).
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