In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called...
31 KB (4,080 words) - 00:19, 9 March 2024
diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. A Hjelmslev quadrilateral is a quadrilateral with...
47 KB (6,758 words) - 00:46, 19 May 2024
Brahmagupta's formula (category Theorems about quadrilaterals and circles)
7th century Indian mathematician, is used to find the area of any cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the...
7 KB (1,331 words) - 09:15, 15 March 2024
of quadrilaterals are inscriptable quadrilateral, inscriptible quadrilateral, inscribable quadrilateral, circumcyclic quadrilateral, and co-cyclic quadrilateral...
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Concyclic points (redirect from Cyclic polygon)
not necessarily concyclic. After triangles, the special case of cyclic quadrilaterals has been most extensively studied. In general the centre O of a...
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Rectangle (redirect from Equiangular quadrilateral)
theorem for cyclic quadrilaterals states that the incentres of the four triangles determined by the vertices of a cyclic quadrilateral taken three at a...
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of the diagonal triangle of a cyclic quadrilateral. The point of intersection of the bimedians of the cyclic quadrilateral belongs to the nine-point circle...
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Law of tangents (section Cyclic quadrilateral)
five-volume work Treatise on the Quadrilateral. A generalization of the law of tangents holds for a cyclic quadrilateral ◻ A B C D . {\displaystyle \square...
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Newton–Gauss line (category Quadrilaterals)
complete quadrilaterals that are associated with cyclic quadrilaterals, based on the work of Barbu and Patrascu. Given any cyclic quadrilateral ABCD, let...
13 KB (1,516 words) - 22:57, 17 December 2022
Ptolemy's theorem (category Theorems about quadrilaterals and circles)
relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named...
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certain triangles inside a cyclic quadrilateral are vertices of a rectangle. Triangulating an arbitrary cyclic quadrilateral by its diagonals yields four...
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special case of Brahmagupta's formula (for the case of a degenerate cyclic quadrilateral). A modern proof, which uses algebra and is quite different from...
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concyclic points. All triangles are cyclic polygons. Cyclic quadrilateral, a special case of a cyclic polygon. Smallest-circle problem, the related problem...
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result in geometry is his formula for cyclic quadrilaterals. Given the lengths of the sides of any cyclic quadrilateral, Brahmagupta gave an approximate and...
45 KB (5,877 words) - 05:24, 7 May 2024
bicentric quadrilaterals have all the properties of both tangential quadrilaterals and cyclic quadrilaterals. Other names for these quadrilaterals are chord-tangent...
24 KB (3,735 words) - 01:17, 23 February 2024
Collinearity (section Quadrilaterals)
tangential quadrilateral are given in Tangential quadrilateral#Collinear points. In a cyclic quadrilateral, the circumcenter, the vertex centroid (the intersection...
18 KB (2,579 words) - 03:53, 24 April 2024
Mollweide's formula (section Cyclic quadrilateral)
regarded as a quadrilateral with one side of length zero. From this perspective, as d {\displaystyle d} approaches zero, a cyclic quadrilateral converges...
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Midpoint (section Quadrilateral)
convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side. If the quadrilateral is...
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the sides of the quadrilateral are the vertices of a cyclic quadrilateral. A convex quadrilateral is orthodiagonal if and only if its Varignon parallelogram...
15 KB (1,714 words) - 02:05, 23 November 2022
Circumcircle (section Cyclic polygons)
called the circumscribed circle, is called a cyclic polygon, or in the special case n = 4, a cyclic quadrilateral. All rectangles, isosceles trapezoids, right...
25 KB (4,549 words) - 07:16, 13 May 2024
geometry, a harmonic quadrilateral, or harmonic quadrangle, is a quadrilateral that can be inscribed in a circle (cyclic quadrilateral) in which the products...
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Circle (section Of certain quadrilaterals)
example is the cyclic quadrilateral. Every regular polygon and every triangle is a cyclic polygon. A polygon that is both cyclic and tangential is called...
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Bisection (section Quadrilateral)
bisector. The internal angle bisectors of a convex quadrilateral either form a cyclic quadrilateral (that is, the four intersection points of adjacent...
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Isosceles right triangle Kepler triangle Scalene triangle Quadrilateral – 4 sides Cyclic quadrilateral Kite Parallelogram Rhombus (equilateral parallelogram)...
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Lexell's theorem (section Cyclic quadrilateral)
constructing a cyclic quadrilateral inside the Lexell circle, using the property that pairs of opposite angles in a spherical cyclic quadrilateral have the...
70 KB (9,226 words) - 14:42, 10 May 2024
consequence of the theorem, opposite angles of cyclic quadrilaterals sum to 180°; conversely, any quadrilateral for which this is true can be inscribed in...
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Kite (geometry) (category Types of quadrilaterals)
kites that are cyclic quadrilaterals, meaning that there is a circle that passes through all their vertices. The cyclic quadrilaterals may equivalently...
38 KB (3,724 words) - 19:10, 10 December 2023
his famous theorem on the diagonals of a cyclic quadrilateral: Brahmagupta's theorem: If a cyclic quadrilateral has diagonals that are perpendicular to...
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Semiperimeter (section For quadrilaterals)
K=rs.} The simplest form of Brahmagupta's formula for the area of a cyclic quadrilateral has a form similar to that of Heron's formula for the triangle area:...
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Isosceles trapezoid (category Types of quadrilaterals)
area can be computed using Brahmagupta's formula for the area of a cyclic quadrilateral, which with two sides equal simplifies to K = ( s − a ) ( s − b )...
9 KB (1,182 words) - 16:30, 9 May 2024