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Gauss-Bodenmiller Theorem

The Circles on the 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 Axis of the Coaxal Circles.

See also Coaxal Circles, Collinear, Complete Quadrilateral, Diagonal (Polygon), Orthocenter, Radical Axis


Johnson, R. A. Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Boston, MA: Houghton Mifflin, p. 172, 1929.

© 1996-9 Eric W. Weisstein