한국   대만   중국   일본 
Miquel Circles -- from Wolfram MathWorld
TOPICS
Search Close
Search

Miquel Circles

DOWNLOAD Mathematica NotebookDownload Wolfram  Notebook
MiquelsTheorem

For a triangle DeltaABC and three points A^', B^', and C^', one on each of its sides, the three Miquel circles are the circles passing through each polygon vertex and its neighboring side points (i.e., AC^'B^', BA^'C^', and CB^'A^'). According to Miquel's theorem , the Miquel circles are concurrent in a point M known as the Miquel point . Similarly, there are n Miquel circles for n lines taken (n-1) at a time.

See also

Clifford's Circle Theorem , Miquel Five Circles Theorem , Miquel Point , Miquel's Theorem , Miquel Triangle

Explore with Wolfram|Alpha

References

Ayme, J.-L. "A Purely Synthetic Proof of the Droz-Farny Line Theorem." Forum Geom. 4 , 219-224, 2004. http://forumgeom.fau.edu/FG2004volume4/FG200426index.html . Honsberger, R. Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., p. 81, 1995. Miquel, A. "Mémoire de Géométrie." Journal de mathématiques pures et appliquées de Liouville 1 , 485-487, 1838.

Referenced on Wolfram|Alpha

Miquel Circles

Cite this as:

Weisstein, Eric W. "Miquel Circles." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/MiquelCircles.html

Subject classifications