Search results
Results from the WOW.Com Content Network
If a cyclic quadrilateral is also orthodiagonal, the distance from the circumcenter to any side equals half the length of the opposite side. [23] In a cyclic orthodiagonal quadrilateral, the distance between the midpoints of the diagonals equals the distance between the circumcenter and the point where the diagonals intersect. [23]
The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals. [1] A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram).
In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. [1] It is named after the Indian mathematician Brahmagupta (598-668). [2]
As is true more generally for any orthodiagonal quadrilateral, the area of a kite may be calculated as half the product of the lengths of the diagonals and : [10] =. Alternatively, the area can be calculated by dividing the kite into two congruent triangles and applying the SAS formula for their area.
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.
A convex quadrilateral is cyclic if and only if opposite angles sum to 180°. Right kite: a kite with two opposite right angles. It is a type of cyclic quadrilateral. Harmonic quadrilateral: a cyclic quadrilateral such that the products of the lengths of the opposing sides are equal. Bicentric quadrilateral: it is both tangential and cyclic.
If the incircle is tangent to the sides AB, BC, CD, DA at T 1, T 2, T 3, T 4 respectively, and if N 1, N 2, N 3, N 4 are the isotomic conjugates of these points with respect to the corresponding sides (that is, AT 1 = BN 1 and so on), then the Nagel point of the tangential quadrilateral is defined as the intersection of the lines N 1 N 3 and N ...
In Euclidean geometry, a harmonic quadrilateral, or harmonic quadrangle, [1] is a quadrilateral that can be inscribed in a circle (cyclic quadrilateral) in which the products of the lengths of opposite sides are equal. It has several important properties.