IMO 1984 LL BEL4

Given a triangle ABC, three equilateral triangles AEB, BFC,

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IMO 1984 LL BEL4

Origin: BEL

Problem

Given a triangle ABC, three equilateral triangles AEB, BFC, and CGA are constructed in the exterior of ABC. Prove that: (a) CE = AF = BG; (b) CE, AF, and BG have a common point.