Extremes with Equilaterals

Geometry Level 5

Two concentric circles with center OO have radii of 2020 and 1414.

Two points AA and BB are drawn such that AA is on the circle of radius 2020, and BB is on the circle with radius 1414.

A point PP is drawn so that APB\triangle APB is equilateral.

If the maximum possible distance of OPOP is MM, and the minimum is mm, then find M×mM\times m.


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