| 单词 | Complete Quadrangle |
| 释义 | Complete QuadrangleIf the four points making up a Quadrilateral are joined pairwise by six distinct lines, a figure known as acomplete 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 ofa complete quadrangle are Collinear on the Radical Line of the Circles on the diameters ofa Quadrilateral. See also Complete Quadrangle, Ptolemy's Theorem
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. |
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