Difference between revisions of "Bodenmiller theorem"
From Encyclopedia of Mathematics
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| − | Consider a complete [[Quadrilateral|quadrilateral]] with four sides | + | {{TEX|done}} |
| + | Consider a complete [[Quadrilateral|quadrilateral]] with four sides $a$, $b$, $c$, $d$ intersecting in the six points $P$, $Q$, $R$, $S$, $T$, $U$. Then the three circles that have the three diagonals $PS$, $QT$ and $RU$ as diagonals intersect in the same two points. | ||
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/b110680a.gif" /> | <img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/b110680a.gif" /> | ||
Revision as of 10:09, 12 April 2014
Consider a complete quadrilateral with four sides $a$, $b$, $c$, $d$ intersecting in the six points $P$, $Q$, $R$, $S$, $T$, $U$. Then the three circles that have the three diagonals $PS$, $QT$ and $RU$ as diagonals intersect in the same two points.
Figure: b110680a
References
| [a1] | R. Fritsch, "Remarks on Bodenmiller's theorem" J. of Geometry , 47 (1993) pp. 23–31 |
| [a2] | G. Weiss, "Eine räumliche Deutung der Vierseiteigenschaft von Bodenmiller" Elemente der Math. , 37 (1982) pp. 21–23 |
How to Cite This Entry:
Bodenmiller theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bodenmiller_theorem&oldid=31611
Bodenmiller theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Bodenmiller_theorem&oldid=31611
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article