cyclic-inscriptable quadrilateral

A bicentric quadrilateral, also called a cyclic-inscriptable quadrilateral, is a four-sided bicentric polygon. The inradius r, circumradius R, and offset x are connected by the equation 1/(R - x)^2 + 1/(R + x)^2 = 1/r^2 (Davis; Durége 1861; Casey 1888, pp. 109-110; Johnson 1929; Dörie 1965; Coolidge 1971, p. 46; Salazar 2006). Finding this relation is sometimes known as Fuss's problem.

bicentric polygon | bicentric triangle | cyclic quadrilateral | Poncelet's porism