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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.

The circle passing through the isodynamic points S and S^' and the triangle centroid G of a triangle DeltaA_1A_2A_3 (Kimberling 1998, pp. 227-228). The Parry circle has ...

Define A^' to be the point (other than the polygon vertex A) where the triangle median through A meets the circumcircle of ABC, and define B^' and C^' similarly. Then the ...

The concurrence S of the Euler lines E_n of the triangles DeltaXBC, DeltaXCA, DeltaXAB, and DeltaABC where X is the incenter. It has equivalent triangle center functions ...

The second de Villiers point is the perspector of the reference triangle and the excenter analog of the BCI triangle, which is Kimberling center X_(1128) has triangle center ...