Miquel Circles


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

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Ayme, J.-L. "A Purely Synthetic Proof of the Droz-Farny Line Theorem." Forum Geom. 4, 219-224, 2004., 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.

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Miquel Circles

Cite this as:

Weisstein, Eric W. "Miquel Circles." From MathWorld--A Wolfram Web Resource.

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