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The Triangle Formed by the Centers of the Miquel Circles

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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 (March 2011)
Open content licensed under CC BY-NC-SA

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

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