A harmonic quadrilateral is a cyclic quadrilateral 
whose side lengths
satisfy
 |
(Gallatly 1910, p. 90). Every harmonic quadrilateral can be transformed into a square by inversion (Gallatly 1910, pp. 92-93).
Harmonic Quadrilateral
See also
Cyclic Quadrilateral, QuadrilateralExplore with Wolfram|Alpha
References
Gallatly, W. "The Harmonic Quadrilateral." §124 and 129 in The Modern Geometry of the Triangle, 2nd ed. London, England: Hodgson, pp. 90 and 92-93, 1910. https://archive.org/details/cu31924001522782.Cite this as:
Weisstein, Eric W. "Harmonic Quadrilateral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HarmonicQuadrilateral.html