MathDB

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?

29