The symmedial circle is the circumcircle of the symmedial triangle. It has circle function
(1)
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which does not correspond to any Kimberling center, and radius
(2)
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where is the circumradius of the reference triangle and
(3)
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Its center has trilinear center function
(4)
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which also does not correspond to any Kimberling center, but lies on the line (P. Moses, pers. comm., Jan. 7, 2005).
The symmedial circle passes through , the center of the Jerabek hyperbola.