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Omni-MATH / We define a binary operation star in the plane as follows: Given two points A and B in the plane, C = A star B is the third vertex of the equilateral triangle ABC oriented positive…

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problem

We define a binary operation $\star$ in the plane as follows: Given two points AA and BB in the plane, $C = A \star B$ is the third vertex of the equilateral triangle ABC oriented positively. What is the relative position of three points I,M,OI, M, O in the plane if $I \star (M \star O) = (O \star I)\star M$ holds?
Plain-text mathematical notation (without MathML)
We define a binary operation $\star$ in the plane as follows: Given two points A and B in the plane, $C = A \star B$ 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 $I \star (M  \star O) = (O \star  I)\star M$ holds?
Original LaTeX notation
We define a binary operation $\star$ in the plane as follows: Given two points $A$ and $B$ in the plane, $C = A \star B$ 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 $I \star (M  \star O) = (O \star  I)\star M$ holds?

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Source and history

task_id
116054a9-8fa6-5f60-9144-aacee7997b61
task_key
test--116054a9-8fa6-5f60-9144-aacee7997b61
task_revision_id
1
config / split
/ test

Official source

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