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- Isogonal_conjugate abstract "In geometry, the isogonal conjugate of a point P with respect to a triangle ABC is constructed by reflecting the lines PA, PB, and PC about the angle bisectors of A, B, and C. These three reflected lines concur at the isogonal conjugate of P. (This definition applies only to points not on a sideline of triangle ABC.)The isogonal conjugate of a point P is sometimes denoted by P*. The isogonal conjugate of P* is P.The isogonal conjugate of the incentre I is itself. The isogonal conjugate of the orthocentre H is the circumcentre O. The isogonal conjugate of the centroid G is (by definition) the symmedian point K. The isogonal conjugates of the Fermat points are the isodynamic points and vice versa. The Brocard points are isogonal conjugates of each other.In trilinear coordinates, if X = x : y : z is a point not on a sideline of triangle ABC, then its isogonal conjugate is 1/x : 1/y : 1/z. For this reason, the isogonal conjugate of X is sometimes denoted by X −1. The set S of triangle centers under trilinear product, defined by (p : q : r) * (u : v : w) = pu : qv : rw,is a commutative group, and the inverse of each X in S is X −1.As isogonal conjugation is a function, it makes sense to speak of the isogonal conjugate of sets of points, such as lines and circles. For example, the isogonal conjugate of a line is a circumconic; specifically, an ellipse, parabola, or hyperbola according as the line intersects the circumcircle in 0, 1, or 2 points. The isogonal conjugate of the circumcircle is the line at infinity. Several well-known cubics (e.g., Thompson cubic, Darboux cubic, Neuberg cubic) are self-isogonal-conjugate, in the sense that if X is on the cubic, then X −1 is also on the cubic.".
- Isogonal_conjugate thumbnail Isogonal_Conjugate.svg?width=300.
- Isogonal_conjugate wikiPageExternalLink IsogonalConjugate.html.
- Isogonal_conjugate wikiPageExternalLink OrthologicPedal.shtml.
- Isogonal_conjugate wikiPageExternalLink isogonal-conjugate_en.html.
- Isogonal_conjugate wikiPageID "2083100".
- Isogonal_conjugate wikiPageLength "2796".
- Isogonal_conjugate wikiPageOutDegree "22".
- Isogonal_conjugate wikiPageRevisionID "675464868".
- Isogonal_conjugate wikiPageWikiLink Altitude_(triangle).
- Isogonal_conjugate wikiPageWikiLink Angle_bisectors.
- Isogonal_conjugate wikiPageWikiLink Bisection.
- Isogonal_conjugate wikiPageWikiLink Brocard_points.
- Isogonal_conjugate wikiPageWikiLink Category:Triangle_geometry.
- Isogonal_conjugate wikiPageWikiLink Central_line_(geometry).
- Isogonal_conjugate wikiPageWikiLink Centroid.
- Isogonal_conjugate wikiPageWikiLink Circumcentre.
- Isogonal_conjugate wikiPageWikiLink Circumcircle.
- Isogonal_conjugate wikiPageWikiLink Circumconic_and_inconic.
- Isogonal_conjugate wikiPageWikiLink Circumscribed_circle.
- Isogonal_conjugate wikiPageWikiLink Concurrent_lines.
- Isogonal_conjugate wikiPageWikiLink Fermat_point.
- Isogonal_conjugate wikiPageWikiLink Geometry.
- Isogonal_conjugate wikiPageWikiLink Incenter.
- Isogonal_conjugate wikiPageWikiLink Incentre.
- Isogonal_conjugate wikiPageWikiLink Isodynamic_point.
- Isogonal_conjugate wikiPageWikiLink Isotomic_conjugate.
- Isogonal_conjugate wikiPageWikiLink Orthocentre.
- Isogonal_conjugate wikiPageWikiLink Point_(geometry).
- Isogonal_conjugate wikiPageWikiLink Reflection_(mathematics).
- Isogonal_conjugate wikiPageWikiLink Symmedian.
- Isogonal_conjugate wikiPageWikiLink Triangle.
- Isogonal_conjugate wikiPageWikiLink Trilinear_coordinates.
- Isogonal_conjugate wikiPageWikiLink File:Isogonal_Conjugate.svg.
- Isogonal_conjugate wikiPageWikiLink File:Isogonal_Conjugate_transform.svg.
- Isogonal_conjugate wikiPageWikiLinkText "Isogonal conjugate".
- Isogonal_conjugate wikiPageWikiLinkText "isogonal conjugate".
- Isogonal_conjugate hasPhotoCollection Isogonal_conjugate.
- Isogonal_conjugate subject Category:Triangle_geometry.
- Isogonal_conjugate comment "In geometry, the isogonal conjugate of a point P with respect to a triangle ABC is constructed by reflecting the lines PA, PB, and PC about the angle bisectors of A, B, and C. These three reflected lines concur at the isogonal conjugate of P. (This definition applies only to points not on a sideline of triangle ABC.)The isogonal conjugate of a point P is sometimes denoted by P*. The isogonal conjugate of P* is P.The isogonal conjugate of the incentre I is itself.".
- Isogonal_conjugate label "Isogonal conjugate".
- Isogonal_conjugate sameAs Isogonal_konjugierte_Punkte.
- Isogonal_conjugate sameAs Conjugado_isogonal.
- Isogonal_conjugate sameAs Isogonaalinen_konjugaatti.
- Isogonal_conjugate sameAs Conjugué_isogonal.
- Isogonal_conjugate sameAs Coniugato_isogonale.
- Isogonal_conjugate sameAs 등각켤레점.
- Isogonal_conjugate sameAs Isogonale_verwantschap.
- Isogonal_conjugate sameAs Sprzężenie_izogonalne.
- Isogonal_conjugate sameAs m.06l05n.
- Isogonal_conjugate sameAs Izogonal_conjugat.
- Isogonal_conjugate sameAs Изогональное_сопряжение.
- Isogonal_conjugate sameAs சமகோண_இணையியம்.
- Isogonal_conjugate sameAs Điểm_liên_hợp_đẳng_giác.
- Isogonal_conjugate sameAs Q1156867.
- Isogonal_conjugate sameAs Q1156867.
- Isogonal_conjugate sameAs 等角共轭.
- Isogonal_conjugate wasDerivedFrom Isogonal_conjugate?oldid=675464868.
- Isogonal_conjugate depiction Isogonal_Conjugate.svg.
- Isogonal_conjugate isPrimaryTopicOf Isogonal_conjugate.