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A set of sides that can form a cyclic quadrilateral can be arranged in any of three distinct sequences each of which can form a cyclic quadrilateral of the same area in the same circumcircle (the areas being the same according to Brahmagupta's area formula). Any two of these cyclic quadrilaterals have one diagonal length in common. [17]: p. 84
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]
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).
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.
Download as PDF; Printable version; In other projects ... Cyclic quadrilateral; Equidiagonal quadrilateral; Kite (geometry) Orthodiagonal quadrilateral. Rhombus ...
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In fact, the incenters form an orthodiagonal cyclic quadrilateral. [1]: p.74 A related result is that the incircles can be exchanged for the excircles to the same triangles (tangent to the sides of the quadrilateral and the extensions of its diagonals). Thus a convex quadrilateral is tangential if and only if the excenters in these four ...
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