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Points which are transformed into each other through Inversion about a given Inversion Circle. The point 
which
is the inverse point of a given point 
with respect to an Inversion Circle 
may be constructed geometrically using
a Compass only (Courant and Robbins 1996).
See also Geometric Construction, Inversion, Polar, Pole (Geometry)
References
Courant, R. and Robbins, H. ``Geometrical Construction of Inverse Points.''
§3.4.3 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed.
Oxford, England: Oxford University Press, pp. 144-145, 1996.