# Extremes with Equilaterals

Geometry Level 5

Two concentric circles with center $O$ have radii of $20$ and $14$.

Two points $A$ and $B$ are drawn such that $A$ is on the circle of radius $20$, and $B$ is on the circle with radius $14$.

A point $P$ is drawn so that $\triangle APB$ is equilateral.

If the maximum possible distance of $OP$ is $M$, and the minimum is $m$, then find $M\times m$.

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