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- Monges_theorem abstract "In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the projective plane. Monge's theorem states that the three such points given by each circle are always in a straight line. In the case of two of the circles being of equal size, the two external tangent lines are parallel. In this case Monge's theorem asserts that the other two intersection points must lie on a line parallel to those two external tangents. In other words if the two external tangents are considered to intersect at the point at infinity, then the other two intersection points must be on a line passing through the same point at infinity, so the line between them takes the same angle as the external tangent.".
- Monges_theorem thumbnail Monge_theorem.svg?width=300.
- Monges_theorem wikiPageExternalLink MongesCircleTheorem.html.
- Monges_theorem wikiPageExternalLink 0486205452.html.
- Monges_theorem wikiPageExternalLink MongeTheorem.shtml.
- Monges_theorem wikiPageExternalLink threecircles.shtml.
- Monges_theorem wikiPageID "14573037".
- Monges_theorem wikiPageLength "3721".
- Monges_theorem wikiPageOutDegree "20".
- Monges_theorem wikiPageRevisionID "702668609".
- Monges_theorem wikiPageWikiLink Category:Articles_containing_proofs.
- Monges_theorem wikiPageWikiLink Category:Circles.
- Monges_theorem wikiPageWikiLink Category:Euclidean_plane_geometry.
- Monges_theorem wikiPageWikiLink Category:Theorems_in_geometry.
- Monges_theorem wikiPageWikiLink Collinearity.
- Monges_theorem wikiPageWikiLink Cut-the-Knot.
- Monges_theorem wikiPageWikiLink Desarguess_theorem.
- Monges_theorem wikiPageWikiLink Gaspard_Monge.
- Monges_theorem wikiPageWikiLink Geometry.
- Monges_theorem wikiPageWikiLink Homothetic_center.
- Monges_theorem wikiPageWikiLink MathWorld.
- Monges_theorem wikiPageWikiLink Menelaus_theorem.
- Monges_theorem wikiPageWikiLink Point_at_infinity.
- Monges_theorem wikiPageWikiLink Problem_of_Apollonius.
- Monges_theorem wikiPageWikiLink Projective_plane.
- Monges_theorem wikiPageWikiLink Tangent_lines_to_circles.
- Monges_theorem wikiPageWikiLink File:Monge_theorem.svg.
- Monges_theorem wikiPageWikiLinkText "Monge's theorem".
- Monges_theorem wikiPageUsesTemplate Template:Cite_book.
- Monges_theorem wikiPageUsesTemplate Template:Reflist.
- Monges_theorem subject Category:Articles_containing_proofs.
- Monges_theorem subject Category:Circles.
- Monges_theorem subject Category:Euclidean_plane_geometry.
- Monges_theorem subject Category:Theorems_in_geometry.
- Monges_theorem hypernym Collinear.
- Monges_theorem type Proof.
- Monges_theorem type Redirect.
- Monges_theorem type Theorem.
- Monges_theorem comment "In geometry, Monge's theorem, named after Gaspard Monge, states that for any three circles in a plane, none of which is inside one of the others, the intersection points of each of the three pairs of external tangent lines are collinear.For any two circles in a plane, an external tangent is a line that is tangent to both circles but does not pass between them. There are two such external tangent lines for any two circles. Each such pair has a unique intersection point in the projective plane.".
- Monges_theorem label "Monge's theorem".
- Monges_theorem sameAs Q2981012.
- Monges_theorem sameAs Mongen_lause.
- Monges_theorem sameAs Մոնժի_թեորեմ.
- Monges_theorem sameAs Twierdzenie_Mongego.
- Monges_theorem sameAs Teorema_de_Monge.
- Monges_theorem sameAs m.03d89yl.
- Monges_theorem sameAs Теорема_Монжа.
- Monges_theorem sameAs Теорема_Монже.
- Monges_theorem sameAs Định_lý_Monge.
- Monges_theorem sameAs Q2981012.
- Monges_theorem wasDerivedFrom Monges_theorem?oldid=702668609.
- Monges_theorem depiction Monge_theorem.svg.
- Monges_theorem isPrimaryTopicOf Monges_theorem.