IMO 1986 LL FRG29

We define a binary operation ⋆in the plane as follows: Given

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IMO 1986 LL FRG29

Origin: FRG

Problem

We define a binary operation ⋆in the plane as follows: Given two points A and B in the plane, C = A ⋆B is the third vertex of the equilateral triangle ABC oriented positively. What is the relative position of three points I, M, O in the plane if I ⋆(M ⋆O) = (O ⋆I) ⋆M holds?