The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle .
Its center has center function
(1)
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where
(2)
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which is not a Kimberling center. The radius is given by
(3)
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where
(4)
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and is the circumradius of the reference triangle.
Its circle function is
(5)
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which is not a Kimberling center.
It passes through Kimberling center , which is also one of two points in which it intersects the nine-point circle, the other point having triangle function
(6)
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(P. Moses, pers. comm., Dec. 31, 2004). Furthermore, the line (which is the radical line of the second Steiner circle and nine-point circle) is parallel to the Euler line of the reference triangle and passes through and .