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if the inscribed one is equilateral then the other is also equilateral

Source: Tuymaada Junior 2002 p2

May 11, 2019
geometryratioEquilateralEquilateral Triangle

Problem Statement

Points on the sides BC BC , CA CA and AB AB of the triangle ABC ABC are respectively A1 A_1 , B1 B_1 and C1 C_1 such that AC1:C1B=BA1:A1C=CB1:B1A=2:1 AC_1: C_1B = BA_1: A_1C = CB_1: B_1A = 2: 1 . Prove that if triangle A1B1C1 A_1B_1C_1 is equilateral, then triangle ABC ABC is also equilateral.
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