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If the given point P lies inside a circle C ,with center O,the circle of radius OP about P intersects C in two points. How to construct point P' inverse to point P with respect to the circle C by the use of the compass alone?


This question is raised from page 144,What is mathematics—2nd Edition

The following content is stated there:

“If the given point P lies inside C the same construction and proof hold, provided that the circle of radius OP about P intersects C in two points.”

I couldn’t understand why does the same construction and proof hold, could you explain it specifically to me?

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    I can do it with compass and straight edge, but you want the construction without straight edge, right?2012-05-17
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    @robjohn You could always just compose your construction with the standard techniques for converting straightedge-and-compass constructions into compass-only?2012-05-17

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