Right kite

A right kite with its circumcircle and incircle. The leftmost and rightmost vertices have right angles.

In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle.[1] That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right angles.[2] If there are exactly two right angles, each must be between sides of different lengths. All right kites are bicentric quadrilaterals (quadrilaterals with both a circumcircle and an incircle), since all kites have an incircle. One of the diagonals (the one that is a line of symmetry) divides the right kite into two right triangles and is also a diameter of the circumcircle.

In a tangential quadrilateral (one with an incircle), the four line segments between the center of the incircle and the points where it is tangent to the quadrilateral partition the quadrilateral into four right kites.

  1. ^ Michael de Villiers, Some Adventures in Euclidean Geometry, ISBN 978-0-557-10295-2, 2009, pp. 154, 206.
  2. ^ De Villiers, Michael (1994), "The role and function of a hierarchical classification of quadrilaterals", For the Learning of Mathematics, 14 (1): 11–18, JSTOR 40248098