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prove that AB=AC in each case

Source: 2023 Viet Nam math olympiad for high school students D1 P7

March 25, 2023
geometry

Problem Statement

Given a triangle ABCABC with symmedians BE,CF(E,FBE,CF(E,F are on the sides CA,AB,CA,AB, respectively)) intersecting at Lemoine point L.L. Prove that: AB=ACAB=AC in each case: a) LB=LC.LB=LC. b) BE=CF.BE=CF.
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