Martin Josefsson, On the inradius of a tangential quadrilateral,
Forum Geometricorum, 10 (2010) 27--34.

Abstract:  We give a survey of known formulas for the inradius r of a tangential quadrilateral, and derive the possibly new formula
 r =  2 Sqrt [(M-uvx)(M-vxy)(M-xyu)(M-yuv)/(uvxy(uv+xy)(ux+vy)(uy+vx))]
where u, v, x and y are the distances from the incenter to the vertices, and M= (uvx+vxy+xyu+yuv)/2.

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