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Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengths equal the semiperimeter of the quadrilateral. [2] The converse implication is also true: whenever a convex quadrilateral has pairs of opposite sides with the same sums of lengths, it has an inscribed circle ...
Bretschneider's formula allows for the calculation of the area of a general quadrilateral if the lengths of all sides are known. Carl Anton Bretschneider (27 May 1808 – 6 November 1878) was a mathematician from Gotha, Germany. Bretschneider worked in geometry, number theory, and history of geometry.
Theorems about quadrilaterals and circles (6 P) Pages in category "Theorems about quadrilaterals" The following 11 pages are in this category, out of 11 total.
Printable version; In other projects ... Space hierarchy theorem ... Varignon's theorem (Euclidean geometry) Vieta's formulas ...
Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]
The ex-tangential quadrilateral is closely related to the tangential quadrilateral (where the four sides are tangent to a circle). Another name for an excircle is an escribed circle, [3] but that name has also been used for a circle tangent to one side of a convex quadrilateral and the extensions of the adjacent two sides. In that context all ...
A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on the perimeter of a square. [7] A diametric quadrilateral is a cyclic quadrilateral having one of its sides as a diameter of the circumcircle. [8] A Hjelmslev quadrilateral is a quadrilateral with two right angles at opposite vertices. [9]
In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any convex cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, Bretschneider's formula, can be used with non-cyclic quadrilateral.
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