Right kite

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.

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.

A special case of right kites are squares, where the diagonals have equal lengths, and the incircle and circumcircle are concentric.

The area of a right kite is The diagonal AC that is a line of symmetry has the length and, since the diagonals are perpendicular (so a right kite is an orthodiagonal quadrilateral with area

The area is given in terms of the circumradius R and the inradius r as[3] If we take the segments extending from the intersection of the diagonals to the vertices in clockwise order to be

The dual polygon to a right kite is an isosceles tangential trapezoid.

[4] If there is only one right angle, it must be between two sides of equal length; in this case, the formulas given above do not apply.