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{{short description|Unique circle centered at a given triangle's orthocenter}} {{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 ...

...ered [[Descartes' theorem]] on the radii of mutually tangent quadruples of circles. ...of the triangle. They can be generalized to additional triples of tangent circles centered at the vertices in which one circle surrounds the other two. ...

...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> ...

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

{{Short description|Great circle with a characteristic length}} {{Use list-defined references|date=June 2024}} ...

{{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. ...

{{Short description|Circle associated with any given triangle}} ...T</math>. It contains the [[circumcenter]]s of the six triangles that are defined inside <math>T</math> by its three [[median (geometry)|median]]s.<ref name= ...

...y]], the '''orthotransversal''' of a point is the [[Line (geometry)|line]] defined as follows.<ref name=":0">{{Cite journal |last=Gibert |first=Bernard |date= For a [[triangle]] {{Mvar|ABC}} and a point {{Mvar|P}}, three '''orthotraces''', intersections of lines {{Mvar|BC ...

{{short description|Conic plane curve associated with a given triangle}} ...o [[extended side|sidelines]] of the reference triangle at vertices of the triangle. ...

{{Short description|Set of circles related by tangency}} ...n circles are shown in blue and red, which are the outermost and innermost circles, respectively.]] ...

...] [[Tiling by regular polygons|by regular polygons]], containing regular [[triangle]]s, [[square]]s, and [[dodecagon]]s, arranged in two [[vertex configuration The ''3.12.12'' vertex figure alone generates a [[truncated hexagonal tiling]], while the ''3.4.3.12'' only exists in this ...

...hematics)|metric]] in a [[normed vector space]] which can be considered as a generalization of both the [[Euclidean distance]] and the [[Manhattan dista ...and taxicab/Manhattan distances for the hypotenuse of a 3-4-5 triangle on a chessboard]] ...

This article tries to give an overview of several coordinate systems in use for the two-dimensional hyperbolic plane. ...determined by a [[distance]] from a reference point and an [[angle]] from a reference direction. ...

[[Image:Unit circle.svg|thumb|alt=Unit circle|Illustration of a unit circle. The variable ''t'' is an [[angle]] measure.]] ...e with radius of 1. Since {{math|1=''C'' = 2''πr''}}, the circumference of a unit circle is {{math|2π}}.]] ...

{{Short description|Part of a line that is bounded by two distinct end points; line with two endpoints}} ...lidean geometry)|intersection]] of all points at or to the right of {{mvar|A}} with all points at or to the left of {{mvar|B}}]] ...

[[File:Reuleaux supporting lines.svg|thumb|A [[Reuleaux triangle]], a [[curve of constant width]] whose area is minimum among all convex sets wit ...at every curve of a given width has area at least as large as the Reuleaux triangle, it is also known as the '''Blaschke–Lebesgue inequality'''.{{r|marmono}} I ...

{{short description|Line which touches a circle at exactly one point}} ...gent lines often involve [[radial line]]s and [[orthogonality|orthogonal]] circles. ...