Orthotransversal

• The orthotransversal of the Feuerbach point is the OI line.{{Cite web |last1=Li4 |last2=S⊗ |last3=和輝 |title=幾何引理維基 |url=https://lii4.github.io/Geometry_Lemma_Wiki.pdf |language=zh}}
• The orthotransversal of the Jerabek center is the Euler line.
• Orthocorrespondents of Fermat points are themselves.{{Cite web |last=dagezjm |title=Pedal triangle |url=https://artofproblemsolving.com/community/q1h2175301p17775874 |website=AoPS}}
• The orthocorrespondent of the Kiepert center X(115) is the focus of the Kiepert parabola X(110).

• There are exactly two points which share the orthoccorespondent.Mathworld Orthocorrespondent. This pair is called the antiorthocorrespondents.
• The orthotransversal of a point on the circumcircle of the reference triangle {{Mvar|ABC}} passes through the circumcenter of {{Mvar|ABC}}. Furthermore, the Steiner line, the orthotransversal, and the trilinear polar are concurrent.{{Cite web |last=Li4 |title=圓錐曲線 |url=https://lii4.github.io/Conic.pdf |language=zh}}
• The orthotransversals of a point P on the Euler line is perpendicular to the line through the isogonal conjugate and the anticomplement of P.{{Cite web |last1=Li4 |last2=S |title=張志煥截線 |url=https://permutation-chang.github.io/Permutationline.pdf |language=zh}}
• The orthotransversal of the nine-point center is perpendicular to the Euler line of the tangential triangle.{{Cite web |last=S |title=正交截線 |url=https://permutation-chang.github.io/Orthotransversal.pdf |language=zh}}
• For the quadrangle {{Mvar|ABCD}}, 4 orthotransversals for each component triangles and each remaining vertexes are concurrent.{{Cite web |title=QA-Tf14: QA-Orthotransversal Point |url=https://chrisvantienhoven.nl/qa-items/qa-transformations/qa-tf14 |access-date=2024-11-02 |website=ENCYCLOPEDIA OF QUADRI-FIGURES (EQF)}}
• Barycentric coordinates of the orthocorrespondent of {{Math|P(p: q: r)}} are

$p(-pS\_A+qS\_B+rS\_C)+a^2qr:q(pS\_A-qS\_B+rS\_C)+b^2rp:r(pS\_A+qS\_B-rS\_C)+c^2pq,$

where {{Mvar|S{{sub|A}},S{{sub|B}},S{{sub|C}}}} are Conway notation.

The Locus of points {{Mvar|P}} that {{Math|P, P{{sup|⊥}}}}, and {{Mvar|Q}} are collinear is a cubic curve. This is called the orthopivotal cubic of {{Mvar|Q}}, {{Math|O(Q)}}.{{Cite web |title=Orthopivotal Cubics |url=http://www.bernard-gibert.fr/gloss/orthopivotalcubi.html |website=Catalogue of Triangle Cubics}} Every orthopivotal cubic passes through two Fermat points.

• {{Math|O(X{{sub|2}})}} is the line at infinity and the Kiepert hyperbola.
• {{Math|O(X{{sub|3}})}} is the Neuberg cubic.{{Cite web |last=Gibert |first=Bernard |title=Neuberg Cubics |url=http://bernard-gibert.fr/files/Resources/neubergs.pdf}}
• The orthopivotal cubic of the vertex is the isogonal image of the Apollonius circle (the Apollonian strophoid{{Cite web |title=K053 |url=http://bernard-gibert.fr/Exemples/k053.html |website=Cubic in Triangle Plane}}).

• Orthocenter
• Orthopole
• Orthologic triangles
• Transversal

{{Reflist}}

• {{cite arXiv|eprint=0807.1131 |last1=Pohoata |first1=Cosmin |last2=Zajic |first2=Vladimir |title=Generalization of the Apollonius Circles |date=2008 |class=math.HO }}
• {{cite arXiv|eprint=1908.11134 |last1=Evers |first1=Manfred |title=On the Geometry of a Triangle in the Elliptic and in the Extended Hyperbolic Plane |date=2019 |class=math.MG }}

• {{MathWorld|title=Orthotransversal|id=Orthotransversal}}
• {{MathWorld|title=Orthocorrespondent|id=Orthocorrespondent}}
• {{Cite web |last=Li4 |title=平面幾何 |url=https://lii4.github.io/Plane_Geometry.pdf |language=zh}}

Category:Triangle geometry

Category:Straight lines defined for a triangle