Editing Inversive geometry (section)

=== Dutta's construction ===
There is a construction of the inverse point to ''A'' with respect to a circle ''Ø'' that is ''independent'' of whether ''A'' is inside or outside ''Ø''.<ref name=SD>Dutta, Surajit (2014) [http://forumgeom.fau.edu/FG2014volume14/FG201422index.html A simple property of isosceles triangles with applications] {{Webarchive|url=https://web.archive.org/web/20180421201921/http://forumgeom.fau.edu/FG2014volume14/FG201422index.html |date=2018-04-21 }}, [[Forum Geometricorum]] 14: 237–240</ref>

Consider a circle ''Ø'' with center ''O'' and a point ''A'' which may lie inside or outside the circle ''Ø''.
* Take the intersection point ''C'' of the ray ''OA'' with the circle ''Ø''.
* Connect the point ''C'' with an arbitrary point ''B'' on the circle ''Ø'' (different from ''C'' and from the point on ''Ø'' antipodal to ''C'')
* Let ''h'' be the reflection of ray ''BA'' in line ''BC''. Then ''h'' cuts ray ''OC'' in a point ''A{{'}}''. ''A{{'}}'' is the inverse point of ''A'' with respect to circle ''Ø''.<ref name=SD/>{{rp|§ 3.2}}