quadrilateral$65961$ - traduction vers allemand
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quadrilateral$65961$ - traduction vers allemand

QUADRILATERAL WHOSE SIDES ARE ALL TANGENT TO A SINGLE CIRCLE INTERIOR TO IT
Inscriptable quadrilateral; Circumscribed quadrilateral; Co-cyclic quadrilateral
  • A bicentric quadrilateral ''ABCD'': the contact quadrilateral (pink) is orthodiagonal.
  • Construction of the Newton line (in red) of a tangential quadrilateral (in blue), showing the alignment of the incenter ''I'', the midpoints of the diagonals ''M''<sub>1</sub> and ''M''<sub>2</sub> and the middle ''M''<sub>3</sub> of the segment ''JK'' (in green) joining the intersection of opposing sides.
  • A tagential quadrilateral (in blue) and its ''contact quadrilateral'' (in green) joining the four contact points between the incircle and the sides. Also shown are the tangency chords joining opposite contact points (in red) and the tangent lengths on the sides
  • 800px
  • Tangential quadrilateral with inradius ''r''
  • left
  • A tangential quadrilateral is partitioned in four triangles meeting at its incenter ''I'', their orthocenters (purple) and the intersection of the diagonals ''P'' (in green) are all colinear,.
  • A tangential quadrilateral with its incircle

quadrilateral      
n. Viereck; mit vier Seiten versehenes Vieleck; Fläche zwischen vier Festungen

Définition

Quadrilateral
·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.

Wikipédia

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.