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Examples of cyclic quadrilaterals. In Euclidean geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral whose vertices all lie on a single circle.This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.
Cyclic quadrilateral. square; kite; Parallelogram. Rhombus (equilateral parallelogram) ... Sierpinski triangle (fractal geometry) Special right triangles; Spiral of ...
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.
[15] [16] The right kites are exactly the kites that are cyclic quadrilaterals, meaning that there is a circle that passes through all their vertices. [17] The cyclic quadrilaterals may equivalently defined as the quadrilaterals in which two opposite angles are supplementary (they add to 180°); if one pair is supplementary the other is as well ...
A set of points lying on the same circle are called concyclic, and a polygon whose vertices are concyclic is called a cyclic polygon. Every triangle is concyclic, but polygons with more than three sides are not in general. Cyclic polygons, especially four-sided cyclic quadrilaterals, have various special properties.
Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. = + In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).
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.
In general, crossed quadrilaterals can have unequal edges. [3] A special form of the antiparallelogram is a crossed rectangle, in which two opposite edges are parallel. [4] Every antiparallelogram is a cyclic quadrilateral, meaning that its four vertices all lie on a single circle. [3]
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