The Compendium Geometry is an eBook providing facts, formulas and explanations about geometry. 
Home Analytic Geometry Quadrilateral Cyclic Quadrilateral  
See also: Quadrilateral  General Definitions, Tangential Quadrilateral  
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Cyclic QuadrilateralA cyclic quadrilateral is a quadrilateral whose vertices lie on a circle. The opposite angles of a cyclic quadrilateral sum to 180 degrees. Please note that the inverse is also true: the vertices of a quadrilateral lie on a circle if the opposite angles sum up to 180°. A quadrilateral that has both an incircle and a circumcircle is known as a bicentric quadrilateral. The length of the diagonals is given by:
d_{1}d_{2} = ac+bd The area A of the cyclic quadrilateral is defined by with s equal to the semiperimeter s = (a+b+c+d)/2. Please note that for any quadrilateral of given side lengths, the area of a cyclic quadrilateral is maximal. The radius r of the circumcircle is given by


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