If the four points making up a Quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results. Note that a complete quadrilateral is defined differently from a Complete Quadrangle.

The midpoints of the sides of any complete quadrangle and the three diagonal points all lie on a Conic known as the Nine-Point Conic. If it is an Orthocentric Quadrilateral, the Conic reduces to a Circle. The Orthocenters of the four Triangles of a complete quadrangle are Collinear on the Radical Line of the Circles on the diameters of a Quadrilateral.

**References**

Coxeter, H. S. M. *Introduction to Geometry, 2nd ed.* New York: Wiley, pp. 230-231, 1969.

Demir, H. ``The Compleat [sic] Cyclic Quadrilateral.'' *Amer. Math. Monthly* **79**, 777-778, 1972.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.* Boston, MA:
Houghton Mifflin, pp. 61-62, 1929.

Ogilvy, C. S. *Excursions in Geometry.* New York: Dover, pp. 101-104, 1990.

© 1996-9

1999-05-26