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The Triangle Formed by the Centers of the Miquel Circles


	Let ABC be a triangle. Let A', B', and C' be points on BC, AC, and AB, respectively. Let A'', B'', and C'' be the circumcenters of AB'C', BA'C', and CA'B', respectively. Then A"B''C'' is similar to ABC.


	Contributed by: Jay Warendorff

See problem 12 in D. R. Davis, Modern College Geometry, Cambridge, MA: Addison-Wesley Press, 1949 p. 161.

Circumcircle (Wolfram MathWorld)

Miquel Circles (Wolfram MathWorld)

Miquel's Theorem (Wolfram MathWorld)

"The Triangle Formed by the Centers of the Miquel Circles" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheTriangleFormedByTheCentersOfTheMiquelCircles/

Contributed by: Jay Warendorff

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