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...ontext of [[triangle geometry]]. It is also referred to as '''Sylvester's (triangle) problem''' in literature, when it is given as a problem rather than a theo ...{{ISBN|978-0-486-46237-0}}, p. 251</ref><ref>Heinrich Dörrie: ''100 Great Problems of Elementary Mathematics''. Dover, 1965, {{ISBN|0486-61348-8}}, S. 142 ([h ...

...ondition for 3 lines with common point to be perpendicular to the sides of triangle}} ...dicular.svg|thumb|upright=1.5|Carnot's theorem: if three perpendiculars on triangle sides intersect in a common point F, then<br/>blue area = red area]] ...

...rrency of lines connecting to certain circles associated with an arbitrary triangle}} [[File:Kosnita points.svg|300px|right|thumb|X(54) is the Kosnita point of the triangle ABC]] ...

...tios larger than <math>\sqrt{3}</math>. The packing fraction of the square-triangle crystal exceeds that of the monoclinic crystal for specific biaxial ellipso * [[Packing problems]] ...

:<math>[\triangle ABP] + [\triangle CDP] = [\triangle ADP] + [\triangle BCP],</math> where {{math|[△{{mvar|ABP}}]}} denotes the area of triangle {{math|△{{mvar|ABP}}}}.{{sfnp|Alsina|Nelsen|2010|pp=[https://books.google.c ...

{{Short description|Set of integers, the lengths of the sides of a triangle with a 60° angle}} ...tein]]) is a set of [[integer]]s which are the lengths of the sides of a [[triangle]] where one of the angles is 60 or 120 degrees. The relation of such triang ...

{{Short description|Circle associated with any given triangle}} ...''van Lamoen circle''' is a special [[circle]] associated with any given [[triangle]] <math>T</math>. It contains the [[circumcenter]]s of the six triangles t ...

{{Short description|Unique curve associated with every triangle}} ...erbach point]], the point of tangency of the [[Incircle and excircles of a triangle|incircle]] and the [[nine-point circle]].<ref>{{Cite journal|last=Boucher|f ...

[[File:Symmetry measure of Reuleaux triangle.svg|thumb|A [[Reuleaux triangle]] and its reflection enclosed by their smallest centrally symmetric convex ...ant width]] with the smallest possible Estermann measure is the [[Reuleaux triangle]].{{r|finch}} ...

...enter–excenter'' or ''excenter–excenter circle'') also passing through two triangle [[vertex (geometry)|vertices]] with its center on the [[circumcircle]].{{r| ...ve Euclidean geometry problems,{{r|chen}} and can be used to reconstruct a triangle starting from one vertex, the incenter, and the circumcenter. ...

...s adventitious angles.svg|thumb|upright=1.0|Solution to Langley's 80-80-20 triangle problem]] ::<math>ABC</math> is an [[isosceles triangle]] with <math>\angle{CBA}=\angle{ACB}=80^\circ.</math> ...

{{Short description|Triangle whose side lengths are consecutive positive integers and area is a positiv ...e side lengths need not necessarily be consecutive integers. A Brahmagupta triangle is called as such in honor of the Indian astronomer and mathematician [[Bra ...

...F</math>, there exists an <math>f\in E\triangle F</math> such that <math>E\triangle\{e,f\}</math> is in the family. For the basis sets of a matroid, the corres ...y role in a characterization of the planar Boolean constraint satisfaction problems that can be solved in polynomial time.{{r|kkr}} ...

{{short description|Unique ellipse tangent to all 3 midpoints of a given triangle's sides}} The Steiner inellipse. According to [[Marden's theorem]], given the triangle with vertices {{math|(1, 7), (7, 5), (3, 1)}}, the [[Focus (geometry)|foci] ...

...in any graph, it is possible to remove twice as many edges as the maximum triangle packing size, and eliminate all triangles. <math>K_5</math> is an extreme c ...nsolved problem in [[graph theory]], a branch of mathematics, concerning [[Triangle graph|triangles]] in [[undirected graph]]s. ...

...ce & Business Media|isbn=9781461209638|language=en}}</ref> such as [[Magic triangle (mathematics)|magic triangles]].<ref>{{Cite web|url=http://recmath.org/Magi ...Magic Triangles.gif|upright=1.8|center|thumb|This displays order 3 [[Magic triangle (mathematics)|magic triangles]], a type of '''magic polygon.''']] ...

..., has at least <math>n-2</math> triangular faces. Thus, three lines form a triangle, four lines form at least two triangles, five lines form at least three tri ...line cuts an existing triangle, one of the resulting two pieces is again a triangle. If it were true more strongly that adding a line always increased the numb ...

...largest centrally symmetric subset (central shaded region) of a [[Reuleaux triangle]] and its reflection across the center of symmetry of the subset]] ...]] with the smallest possible Kovner–Besicovitch measure is the [[Reuleaux triangle]].{{r|finch}} ...

...solved using mass point geometry can also be solved using either [[similar triangle]]s, [[Euclidean vector|vectors]], or area ratios,<ref>{{Cite web |url=http: ...ratios of lengths to calculate the ratio of areas between a triangle and a triangle formed by three cevians. ...

...colored with one of three colors, it must be possible to regroup the nine triangle vertices into three "rainbow" triangles having one vertex of each color. Th ...''S''|&nbsp;≤&nbsp;2 or ''S'' forms the three vertices of a non-degenerate triangle. For this linear algebra and this matroid, the bases are exactly the non-de ...