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Construct P*, which is a 90 degree rotation of P around O followed by a 2x dilation.
It is possible to solve this with compass and ruler alone. But the following
procedure is easier. Construct in this order
- The line through P and O.
- The perpendicular to this line at O.
- The fixed circle at O with radius 2*d(P,O).
The intersection of the circle and perpendicular line is the required point P*.
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