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midpoint wanted, equilateral triangles on sides of a triangle related

Source: 2006 Oral Moscow Geometry Olympiad grades 8-9 p5

October 17, 2020
geometrymidpointEquilateral

Problem Statement

Equilateral triangles ABC1,BCA1,CAB1ABC_1, BCA_1, CAB_1 are built on the sides of the triangle ABCABC to the outside. On the segment A1B1A_1B_1 to the outer side of the triangle A1B1C1A_1B_1C_1, an equilateral triangle A1B1C2A_1B_1C_2 is constructed. Prove that CC is the midpoint of the segment C1C2C_1C_2.
(A. Zaslavsky)
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