Albrecht Hess, On a circle containing the incenters of tangential quadrilaterals,
Forum Geometricorum, 14 (2014) 389--396.

Abstract. When we fix one side and draw different tangential quadrilaterals having the same side lengths but different angles we observe that their incenters lie on a circle. Based on a known formula expressing the incircle radius of a tangential quadrilateral by its tangent lengths, some older results will be presented in a new light and the equation of the before mentioned circle will appear. This circle encodes information about tangential and bicentric quadrilaterals that leads to an apparently new characterization of tangential quadrilaterals. Curiously enough, no trigonometric formulae are needed.

[ps file] [pdf]