Cosa (chi) è quadrilateral$65961$ - definizione

QUADRILATERAL WHOSE SIDES ARE ALL TANGENT TO A SINGLE CIRCLE INTERIOR TO IT

Inscriptable quadrilateral; Circumscribed quadrilateral; Co-cyclic quadrilateral

Saccheri quadrilateral

QUADRILATERAL WITH TWO EQUAL SIDES PERPENDICULAR TO THE BASE

Khayyam-Saccheri quadrilateral; Saccheri Quadrilateral; Khayyam–Saccheri quadrilateral; Khayyam quadrilateral

A Saccheri quadrilateral (also known as a Khayyam–Saccheri quadrilateral) is a quadrilateral with two equal sides perpendicular to the base. It is named after Giovanni Gerolamo Saccheri, who used it extensively in his book Euclides ab omni naevo vindicatus (literally Euclid Freed of Every Flaw) first published in 1733, an attempt to prove the parallel postulate using the method Reductio ad absurdum.

https://en.wikipedia.org/wiki/Saccheri_quadrilateral

Ex-tangential quadrilateral

CONVEX QUADRILATERAL WHERE THE EXTENSIONS OF ALL FOUR SIDES ARE TANGENT TO A CIRCLE OUTSIDE IT

Extangential quadrilateral

In Euclidean geometry, an ex-tangential quadrilateral is a convex quadrilateral where the extensions of all four sides are tangent to a circle outside the quadrilateral.Radic, Mirko; Kaliman, Zoran and Kadum, Vladimir, "A condition that a tangential quadrilateral is also a chordal one", Mathematical Communications, 12 (2007) pp.

https://en.wikipedia.org/wiki/Ex-tangential_quadrilateral

Quadrilateral

POLYGON WITH FOUR SIDES

Tetragon; Quadrilaterals; Quadrialateral; Quadrilateralness; 4-gon; Crossed-quadrilateral; Butterfly-quadrilateral; Bowtie-quadrilateral; Cross quadrilateral; Cross-quadrilateral; Quadragon; Irregular quadrilateral; Maltitude; Crossed quadrilateral; Bimedian; Skew quadrilateral; Concave quadrilateral; Quadrilater

·adj Having four sides, and consequently four angles; quadrangular.

II. Quadrilateral ·noun A plane figure having four sides, and consequently four angles; a quadrangular figure; any figure formed by four lines.

III. Quadrilateral ·noun An area defended by four fortresses supporting each other; as, the Venetian quadrilateral, comprising Mantua, Peschiera, Verona, and Legnano.

Wikipedia

Tangential quadrilateral

In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral. This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius is called the inradius. Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called circumscribable quadrilaterals, circumscribing quadrilaterals, and circumscriptible quadrilaterals. Tangential quadrilaterals are a special case of tangential polygons.

Other less frequently used names for this class of quadrilaterals are inscriptable quadrilateral, inscriptible quadrilateral, inscribable quadrilateral, circumcyclic quadrilateral, and co-cyclic quadrilateral. Due to the risk of confusion with a quadrilateral that has a circumcircle, which is called a cyclic quadrilateral or inscribed quadrilateral, it is preferable not to use any of the last five names.

All triangles can have an incircle, but not all quadrilaterals do. An example of a quadrilateral that cannot be tangential is a non-square rectangle. The section characterizations below states what necessary and sufficient conditions a quadrilateral must satisfy to be able to have an incircle.

https://en.wikipedia.org/wiki/Tangential quadrilateral