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Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters O_(AB), O_(BA), etc. of the six circumcircles of these smaller triangles ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...

The hexyl circle is the circumcircle of the hexyl triangle. Amazingly, its center is at the incenter I and its radius is 2R, where R is the circumradius. Its circle function ...

The Lucas central circle is the circumcircle of the Lucas central triangle. The center, radius, and circle function appear to be complicated, and neither the center nor the ...

The symmedial circle is the circumcircle of the symmedial triangle. It has circle function l=(bc(a^4-a^2b^2-b^4-a^2c^2-b^2c^2-c^4))/(2(a^2+b^2)(a^2+c^2)(b^2+c^2)), (1) which ...

The Mandart circle is the circumcircle of the extouch triangle. It has center at Kimberling center X_(1158), which has trilinear center function (1) and radius ...

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

The incentral circle is the circumcircle of the incentral triangle. It has radius R_I=(sqrt(abcf(a,b,c)f(b,c,a)f(c,a,b)))/(8Delta(a+b)(a+c)(b+c)), (1) where Delta is the area ...

A point v is a central point of a graph if the eccentricity of the point equals the graph radius. The set of all central points is called the graph center.

The extremities of parallel radii of two circles are called homologous with respect to the similitude center collinear with them.