Crossword Solver > found answer > BICENTRICQUADRILATERAL (bicentric quadrilateral)

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bicentricquadrilateral

bicentric quadrilateral

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Definitions of bicentric quadrilateral in various dictionaries:

BICENTRIC QUADRILATERAL - In Euclidean geometry, a bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and center of thes...

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Bicentric quadrilateral might refer to
In Euclidean geometry, a Bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and center of these circles are called inradius and circumradius, and incenter and circumcenter respectively. From the definition it follows that bicentric quadrilaterals have all the properties of both tangential quadrilaterals and cyclic quadrilaterals. Other names for these quadrilaterals are chord-tangent quadrilateral and inscribed and circumscribed quadrilateral. It has also rarely been called a double circle quadrilateral and double scribed quadrilateral.If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle. This is a corollary of Poncelet's porism, which was proved by the French mathematician Jean-Victor Poncelet (1788–1867).

Bicentric quadrilateral might refer to

In Euclidean geometry, a Bicentric quadrilateral is a convex quadrilateral that has both an incircle and a circumcircle. The radii and center of these circles are called inradius and circumradius, and incenter and circumcenter respectively. From the definition it follows that bicentric quadrilaterals have all the properties of both tangential quadrilaterals and cyclic quadrilaterals. Other names for these quadrilaterals are chord-tangent quadrilateral and inscribed and circumscribed quadrilateral. It has also rarely been called a double circle quadrilateral and double scribed quadrilateral.If two circles, one within the other, are the incircle and the circumcircle of a bicentric quadrilateral, then every point on the circumcircle is the vertex of a bicentric quadrilateral having the same incircle and circumcircle. This is a corollary of Poncelet's porism, which was proved by the French mathematician Jean-Victor Poncelet (1788–1867).

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