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{{Short description|Special triangle based on arbitrary triangle}} ...d): <math>\triangle M^\prime_c M^\prime_b M^\prime_a </math> <br/> mid arc points: <math>M_a, M_b, M_c </math>]] ...

{{short description|Line tangent to a given triangle's circumcircle at one its vertices}} {{legend-line|solid #4169E1|Reference triangle {{math|△''ABC''}}}} ...

...cumcircle: <math>O</math> <br/> the green segments are used in the formula for radius]] [[File:Isogonal points pedal circle.svg|thumb|upright=1.4|<math>\triangle ABC</math> with isogonal conjugates <math>P</math> and <math>Q</math> <br/> ...

{{short description|Triangle center}} ...ngle to the points of [[tangency]] formed by the opposing [[excircle]] and a larger circle that [[Problem of Apollonius|is tangent to all three excircle ...

...endiculars <math>P_{ab},P_{ac},P_{ba}, P_{bc},P_{ca},P_{cb} </math> lie on a common circle]] ...rench mathematician [[Eutaris]] in 1877.<ref>[https://www.cut-the-knot.org/triangle/Taylor.shtml Taylor-Kreis] at cut-the-knot.org (retrieved 2024-0-2-9)</ref> ...

{{short description|Triangle related to a given triangle by two functions}} ...e center function]]. The [[excentral triangle]] is an example of a central triangle. The central triangles have been classified into three types based on the p ...

{{Short description|Circle constructed from a triangle}} [[File:Orthocentroidal disk.svg|thumb|360px|A triangle (black), its [[orthocenter]] (blue), its [[centroid]] (red), and its orthoc ...

...ne point (the intersection of the symmedians) of the triangle. The Brocard points, <math>\Omega_1</math>​ and <math>\Omega_2</math>​, are symmetric with resp [[File:Aguilera-Brocard Triangle in the Brocard Circle.png|thumb|262x262px|Ilustration of the Aguilera-Broca ...

{{short description|Axis of perspectivity of a given triangle, its cevian triangle, and some point}} ...ineer and mathematician, who introduced the idea of the trilinear polar of a point in 1865.<ref name="Coxeter"/><ref>{{cite book|last=Coxeter|first=H.S. ...

...bn=978-0-387-94826-3 }}</ref> and is so named for its resemblance to the [[triangle inequality]]. It is an important lemma in the proof of the [[Plünnecke-Ruzs <!-- The referenced article on the Plünnecke-Ruzsa inequality is currently a draft and has been submitted concurrently with this one. --> ...

{{short description|Hyperbola constructed from a given triangle and point}} {{legend|blue|Points of triangle {{math|△''ABC''}} and given point {{mvar|P}}}} ...

{{short description|Plane curve associated with any triangle}} ...ics]] which is a compilation of extensive information about more than 1200 triangle cubics. ...

{{short description|Circle tangent to two sides of a triangle and its circumcircle}} ...math>A</math> is called the ''<math>A</math>-mixtilinear incircle.'' Every triangle has three unique mixtilinear incircles, one corresponding to each vertex. ...

...y]], the '''orthotransversal''' of a point is the [[Line (geometry)|line]] defined as follows.<ref name=":0">{{Cite journal |last=Gibert |first=Bernard |date= ...ar|P}} respectively are [[collinear]]. The line which includes these three points is called the '''orthotransversal''' of {{Mvar|P}}. ...

...}}, ''B''{{sub|2}}, ''C''{{sub|1}}}} and {{Math|''C''{{sub|2}}}} similarly for {{Mvar|CA}} and {{Mvar|AB}}. If \angle A=\angle AB_1C_1=AC_2B_2, ...

{{Short description|Circumellipse of a triangle whose center is the triangle's centroid}} ...edians]], each [[bisection|bisecting]] a side. The medians coincide at the triangle's [[centroid]], which is also the center of the Steiner ellipse.]] ...

{{Short description|Conic curves associated with a triangle}} ...a [[parabola]], called the '''Kiepert parabola'''. The Kiepert conics are defined as follows: ...

...ir centers are the '''Soddy centers''' of the triangle. They are all named for [[Frederick Soddy]], who rediscovered [[Descartes' theorem]] on the radii o ...triangle. These circles are related to many other notable features of the triangle. They can be generalized to additional triples of tangent circles centered ...

...rt description|Geometric property of certain lines with respect to a given triangle}} ...690608}}</ref><ref name=TCCT>{{cite book|last=Kimberling|first=Clark|title=Triangle Centers and Central Triangles|publisher=Utilitas Mathematica Publishing, In ...

{{Short description|Method of calculating ray-triangle intersections in 3D space}} ...//www.lighthouse3d.com/tutorials/maths/ray-triangle-intersection|title=Ray-Triangle Intersection|date=26 March 2011 |publisher=lighthouse3d|accessdate=2017-09- ...