# Bodenmiller theorem

From Encyclopedia of Mathematics

Consider a complete quadrilateral with four sides , , , intersecting in the six points , , , , , . Then the three circles that have the three diagonals , and 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=13366

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