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In a cyclic orthodiagonal quadrilateral, the anticenter coincides with the point where the diagonals intersect. [2] Brahmagupta's theorem states that for a cyclic orthodiagonal quadrilateral, the perpendicular from any side through the point of intersection of the diagonals bisects the opposite side. [2]
In a cyclic orthodiagonal quadrilateral, the anticenter coincides with the point where the diagonals intersect. [23] Brahmagupta's theorem states that for a cyclic quadrilateral that is also orthodiagonal, the perpendicular from any side through the point of intersection of the diagonals bisects the opposite side. [23]
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 tangential quadrilaterals that are also orthodiagonal. [3] A right kite is a kite with a circumcircle. If a quadrilateral is both tangential and cyclic, it is called a bicentric quadrilateral, and if it is both tangential and a trapezoid, it is called a tangential trapezoid.
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. Orthodiagonal quadrilateral: the diagonals cross at right angles. Equidiagonal quadrilateral: the diagonals are of equal length.
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.
Every kite is an orthodiagonal quadrilateral, meaning that its two diagonals are at right angles to each other. Moreover, one of the two diagonals (the symmetry axis) is the perpendicular bisector of the other, and is also the angle bisector of the two angles it meets. [1]
A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing circle or circumcircle. All concyclic points are equidistant from the center of the circle. Three points in the plane that do not all fall on a straight line are concyclic, so every triangle is a cyclic polygon, with a well-defined ...