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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