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- Limiting_point_(geometry) abstract "In geometry, the limiting points of two disjoint circles A and B in the Euclidean plane are points p that may be defined by any of the following equivalent properties:The pencil of circles defined by A and B contains a degenerate (radius zero) circle centered at p.Every circle or line that is perpendicular to both A and B passes through p.An inversion centered at p transforms A and B into concentric circles.The midpoint of the two limiting points is the point where the radical axis of A and B crosses the line through their centers. This intersection point has equal power distance to all the circles in the pencil containing A and B. The limiting points themselves can be found at this distance on either side of the intersection point, on the line through the two circle centers. From this fact it is straightforward to construct the limiting points algebraically or by compass and straightedge.An explicit formula expressing the limiting points as the solution to a quadratic equation in the coordinates of the circle centers and their radii is given by Weisstein.Inverting one of the two limiting points through A or B produces the other limiting point. An inversion centered at one limiting point maps the other limiting point to the common center of the concentric circles.".
- Limiting_point_(geometry) thumbnail Apollonian_circles.svg?width=300.
- Limiting_point_(geometry) wikiPageID "41144612".
- Limiting_point_(geometry) wikiPageLength "2905".
- Limiting_point_(geometry) wikiPageOutDegree "12".
- Limiting_point_(geometry) wikiPageRevisionID "583147243".
- Limiting_point_(geometry) wikiPageWikiLink Apollonian_circles.
- Limiting_point_(geometry) wikiPageWikiLink Category:Circles.
- Limiting_point_(geometry) wikiPageWikiLink Category:Inversive_geometry.
- Limiting_point_(geometry) wikiPageWikiLink Compass-and-straightedge_construction.
- Limiting_point_(geometry) wikiPageWikiLink Compass_and_straightedge.
- Limiting_point_(geometry) wikiPageWikiLink Concentric.
- Limiting_point_(geometry) wikiPageWikiLink Euclidean_plane.
- Limiting_point_(geometry) wikiPageWikiLink Inversive_geometry.
- Limiting_point_(geometry) wikiPageWikiLink Pencil_of_circles.
- Limiting_point_(geometry) wikiPageWikiLink Perpendicular.
- Limiting_point_(geometry) wikiPageWikiLink Power_distance.
- Limiting_point_(geometry) wikiPageWikiLink Quadratic_equation.
- Limiting_point_(geometry) wikiPageWikiLink Radical_axis.
- Limiting_point_(geometry) wikiPageWikiLink Two-dimensional_space.
- Limiting_point_(geometry) wikiPageWikiLink File:Apollonian_circles.svg.
- Limiting_point_(geometry) wikiPageWikiLinkText "Limiting point (geometry)".
- Limiting_point_(geometry) wikiPageWikiLinkText "limiting points".
- Limiting_point_(geometry) hasPhotoCollection Limiting_point_(geometry).
- Limiting_point_(geometry) wikiPageUsesTemplate Template:Elementary-geometry-stub.
- Limiting_point_(geometry) wikiPageUsesTemplate Template:Reflist.
- Limiting_point_(geometry) subject Category:Circles.
- Limiting_point_(geometry) subject Category:Inversive_geometry.
- Limiting_point_(geometry) hypernym P.
- Limiting_point_(geometry) type Album.
- Limiting_point_(geometry) comment "In geometry, the limiting points of two disjoint circles A and B in the Euclidean plane are points p that may be defined by any of the following equivalent properties:The pencil of circles defined by A and B contains a degenerate (radius zero) circle centered at p.Every circle or line that is perpendicular to both A and B passes through p.An inversion centered at p transforms A and B into concentric circles.The midpoint of the two limiting points is the point where the radical axis of A and B crosses the line through their centers. ".
- Limiting_point_(geometry) label "Limiting point (geometry)".
- Limiting_point_(geometry) sameAs m.0zbv299.
- Limiting_point_(geometry) sameAs Q17077751.
- Limiting_point_(geometry) sameAs Q17077751.
- Limiting_point_(geometry) wasDerivedFrom Limiting_point_(geometry)?oldid=583147243.
- Limiting_point_(geometry) depiction Apollonian_circles.svg.
- Limiting_point_(geometry) isPrimaryTopicOf Limiting_point_(geometry).