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- Power_center_(geometry) abstract "In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical axes of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles orthogonally; the construction of this orthogonal circle corresponds to Monge's problem. This is a special case of the three conics theorem.The three radical axes meet in a single point, the radical center, for the following reason. The radical axis of a pair of circles is defined as the set of points that have equal power h with respect to both circles. For example, for every point P on the radical axis of circles 1 and 2, the powers to each circle are equal, h1 = h2. Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h2 = h3. Therefore, at the intersection point of these two lines, all three powers must be equal, h1 = h2 = h3. Since this implies that h1 = h3, this point must also lie on the radical axis of circles 1 and 3. Hence, all three radical axes pass through the same point, the radical center.The radical center has several applications in geometry. It has an important role in a solution to Apollonius' problem published by Joseph Diaz Gergonne in 1814. In the power diagram of a system of circles, all of the vertices of the diagram are located at radical centers of triples of circles. The Spieker center of a triangle is the radical center of its excircles. Several types of radical circles have been defined as well, such as the radical circle of the Lucas circles.".
- Power_center_(geometry) thumbnail Radical_center.svg?width=300.
- Power_center_(geometry) wikiPageExternalLink RadicalAxis.shtml.
- Power_center_(geometry) wikiPageExternalLink RadicalCenter.shtml.
- Power_center_(geometry) wikiPageID "326298".
- Power_center_(geometry) wikiPageLength "4435".
- Power_center_(geometry) wikiPageOutDegree "21".
- Power_center_(geometry) wikiPageRevisionID "636075714".
- Power_center_(geometry) wikiPageWikiLink Category:Elementary_geometry.
- Power_center_(geometry) wikiPageWikiLink Category:Geometric_centers.
- Power_center_(geometry) wikiPageWikiLink Circle.
- Power_center_(geometry) wikiPageWikiLink Cut-the-Knot.
- Power_center_(geometry) wikiPageWikiLink Geometry.
- Power_center_(geometry) wikiPageWikiLink Harold_Scott_MacDonald_Coxeter.
- Power_center_(geometry) wikiPageWikiLink Incircle_and_excircles_of_a_triangle.
- Power_center_(geometry) wikiPageWikiLink Joseph_Diaz_Gergonne.
- Power_center_(geometry) wikiPageWikiLink Lucas_circle.
- Power_center_(geometry) wikiPageWikiLink Mathematical_Association_of_America.
- Power_center_(geometry) wikiPageWikiLink Power_diagram.
- Power_center_(geometry) wikiPageWikiLink Power_of_a_point.
- Power_center_(geometry) wikiPageWikiLink Problem_of_Apollonius.
- Power_center_(geometry) wikiPageWikiLink Radical_axis.
- Power_center_(geometry) wikiPageWikiLink Samuel_L._Greitzer.
- Power_center_(geometry) wikiPageWikiLink Spieker_center.
- Power_center_(geometry) wikiPageWikiLink Three_conics_theorem.
- Power_center_(geometry) wikiPageWikiLink Triangle.
- Power_center_(geometry) wikiPageWikiLink Washington,_D.C..
- Power_center_(geometry) wikiPageWikiLink File:Radical_center.svg.
- Power_center_(geometry) wikiPageWikiLinkText "Power center (geometry)".
- Power_center_(geometry) wikiPageWikiLinkText "Power center".
- Power_center_(geometry) wikiPageWikiLinkText "power center (geometry)".
- Power_center_(geometry) wikiPageWikiLinkText "radical center".
- Power_center_(geometry) wikiPageWikiLinkText "radical circle".
- Power_center_(geometry) title "Monge's problem".
- Power_center_(geometry) title "Radical center".
- Power_center_(geometry) title "Radical circle".
- Power_center_(geometry) urlname "MongesProblem".
- Power_center_(geometry) urlname "RadicalCenter".
- Power_center_(geometry) urlname "RadicalCircle".
- Power_center_(geometry) wikiPageUsesTemplate Template:Cite_book.
- Power_center_(geometry) wikiPageUsesTemplate Template:Commons_category.
- Power_center_(geometry) wikiPageUsesTemplate Template:Mathworld.
- Power_center_(geometry) wikiPageUsesTemplate Template:Reflist.
- Power_center_(geometry) subject Category:Elementary_geometry.
- Power_center_(geometry) subject Category:Geometric_centers.
- Power_center_(geometry) hypernym Point.
- Power_center_(geometry) type Place.
- Power_center_(geometry) type Center.
- Power_center_(geometry) comment "In geometry, the power center of three circles, also called the radical center, is the intersection point of the three radical axes of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of the unique circle (the radical circle) that intersects the three given circles orthogonally; the construction of this orthogonal circle corresponds to Monge's problem.".
- Power_center_(geometry) label "Power center (geometry)".
- Power_center_(geometry) sameAs Q5254628.
- Power_center_(geometry) sameAs Centro_radical.
- Power_center_(geometry) sameAs Potentzia-zentro.
- Power_center_(geometry) sameAs m.01w5h1.
- Power_center_(geometry) sameAs Centru_radical.
- Power_center_(geometry) sameAs Радикальный_центр.
- Power_center_(geometry) sameAs சமதொடுகோட்டச்சுச்_சந்தி.
- Power_center_(geometry) sameAs Q5254628.
- Power_center_(geometry) wasDerivedFrom Power_center_(geometry)?oldid=636075714.
- Power_center_(geometry) depiction Radical_center.svg.
- Power_center_(geometry) isPrimaryTopicOf Power_center_(geometry).