If the four points making up a quadrilateral are joined pairwise by six distinct lines, a figure known as a complete quadrangle results.
A complete quadrangle is therefore a set of four points, no three collinear, and
the six lines which join them. Note that a complete
quadrilateral is different 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 .
See also Complete Quadrilateral ,
Ptolemy's Theorem
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References Coxeter, H. S. M. Introduction to Geometry, 2nd ed. Demir,
H. "The Compleat [sic] Cyclic Quadrilateral." Amer. Math. Monthly 79 ,
777-778, 1972. Durell, C. V. Modern
Geometry: The Straight Line and Circle. Graustein,
W. C. Introduction
to Higher Geometry. Johnson,
R. A. Modern
Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle. Ogilvy, C. S.
Excursions
in Geometry. Referenced
on Wolfram|Alpha Complete Quadrangle
Cite this as:
Weisstein, Eric W. "Complete Quadrangle."
From MathWorld https://mathworld.wolfram.com/CompleteQuadrangle.html
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