Bodenmiller theorem

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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


[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
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Bodenmiller theorem. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article