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21-DoubledCircle
You may drag any of the red points, and the construction will adjust accordingly.

Explanation of the construction: If the radius of the original circle is r and the radius of the double-area circle is s, then we need pi*s^2 = 2*pi*r^2, or s = 2*sqrt(r). The Pythagorean Theorem gives that the hypoteneuse FB has length 2*sqrt(r).

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