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...every continuous transformation of the plane that preserves all Apollonius quadrilaterals must be a Möbius transformation.{{r|harras}} ...is an Apollonius quadrilateral. [[Cyclic quadrilateral|Cyclic]] Apollonius quadrilaterals, inscribed in a given [[circle]], may be constructed by choosing two opposi ...

...] to the same [[inscribed circle]]. Pitot's theorem states that, for these quadrilaterals, the two sums of lengths of opposite sides are the same. Both sums of lengt ...edu/FG2011volume11/FG201108.pdf|title=More characterizations of tangential quadrilaterals|journal=Forum Geometricorum|volume=11|year=2011|pages=65–82|mr=2877281|acce ...

...nal quadrilaterals were important in ancient [[Indian mathematics]], where quadrilaterals were classified first according to whether they were equidiagonal and then Examples of equidiagonal quadrilaterals include the [[isosceles trapezoid]]s, [[rectangle]]s and [[Square (geometry ...

Quadrilaterals may also have Coxeter decompositions. *A quadrilateral can be decomposed by quadrilaterals. ...

...lic, then <math> Q^{(2)} </math> is not degenerate.<ref name=King>J. King, Quadrilaterals formed by perpendicular bisectors, in ''Geometry Turned On'', (ed. J. King) ...ndicular bisector construction, ''Geom. Dedicata'', 56 (1995) 75–84.</ref> Quadrilaterals <math> Q^{(2)} </math> and <math> Q^{(4)} </math> are also homothetic. ...

...cause of the latter the restatement of the Pythagorean theorem in terms of quadrilaterals is occasionally called the '''Euler–Pythagoras theorem'''. ...[cycle graph]].<ref>Geoffrey A. Kandall: ''Euler's Theorem for Generalized Quadrilaterals''. The College Mathematics Journal, Vol. 33, No. 5 (Nov., 2002), pp. 403–40 ...

|title=The role and function of a hierarchical classification of quadrilaterals ...es of different lengths. All right kites are [[bicentric quadrilateral]]s (quadrilaterals with both a circumcircle and an incircle), since all kites have an [[incirc ...

...n easily be derived from [[Anne's theorem]] considering that in tangential quadrilaterals the combined lengths of opposite sides are equal ([[Pitot theorem]]: ''a''& [[Category:Theorems about quadrilaterals and circles]] ...

| title = A Cornucopia of Quadrilaterals [[Category:Theorems about quadrilaterals]] ...

...ve the maximum [[area]] for their [[diameter of a set|diameter]] among all quadrilaterals, solving the <math>n=4</math> case of the [[biggest little polygon]] proble | title = A Cornucopia of Quadrilaterals ...

...ow that this theorem is a consequence of the [[Japanese theorem for cyclic quadrilaterals]].<ref>[https://www.cut-the-knot.org/Curriculum/Geometry/Eyeball.shtml ''Th * [[Japanese theorem for cyclic quadrilaterals]] ...

==Quadrilaterals== ...als, which has area <math>\tfrac12</math>. Infinitely many other midsquare quadrilaterals also have diameter one and have the same area as the square, so in this cas ...

=== Quadrilaterals=== [[File:Symmetries of square.svg|thumb|Quadrilaterals by symmetry]] ...

...Alexander Bogomolny|Bogomolny, Alexander]], "Inscriptible and Exscriptible Quadrilaterals", ''Interactive Mathematics Miscellany and Puzzles'', [http://www.cut-the-k ...Martin, ''Similar Metric Characterizations of Tangential and Extangential Quadrilaterals'', Forum Geometricorum Volume 12 (2012) pp. 63-77 [http://forumgeom.fau.edu ...

===Cyclogons generated by quadrilaterals=== ...

== Complete quadrilaterals == == Applications to cyclic quadrilaterals== ...

...iagonal quadrilateral (yellow). According to the characterization of these quadrilaterals, the two red [[square]]s on two opposite sides of the quadrilateral have th ...s, the kites are the [[tangential quadrilateral|tangential]] orthodiagonal quadrilaterals.<ref>{{citation ...

...in a geometric progression.<ref name=Buchholz>{{Cite journal |title=Heron Quadrilaterals with sides in Arithmetic or Geometric progression |last1=Buchholz |first1=R ...uadrilateral.svg|thumb|right|300px|alt=Two 7-Con quadrilaterals.|Two 7-Con quadrilaterals.]] ...

...for [[Polygon|''n''-gons]], then this area equality also holds for complex quadrilaterals.<ref name=Coxeter>[[Coxeter|Coxeter, H. S. M.]] and Greitzer, S. L. "Quadra ...s (mathematics)|barycentric coordinates]]. The proof applies even to skew quadrilaterals in spaces of any dimension. ...