The Dou circle is the circle cutting the sidelines of the reference triangle at , , , , , and such that (i.e., all are right angles).
Its center is Kimberling center with center function
(1)
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and its radius is
(2)
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where is the circumradius of the reference triangle and is an 18th-degree polynomial.
It has circle function
(3)
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which does not correspond to any Kimberling center.
No Kimberling centers lie on the Dou circle.