The circles on the polygon diagonals of a complete quadrilateral as diameters are coaxal. Furthermore, the orthocenters of the four triangles of a complete quadrilateral are collinear on the radical line of the coaxal circles.
Gauss-Bodenmiller Theorem
See also
Coaxal Circles, Collinear, Complete Quadrilateral, Orthocenter, Polygon Diagonal, Radical LineExplore with Wolfram|Alpha
References
Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 172, 1929.Referenced on Wolfram|Alpha
Gauss-Bodenmiller TheoremCite this as:
Weisstein, Eric W. "Gauss-Bodenmiller Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Gauss-BodenmillerTheorem.html