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If G is a perfect group, then the group center of the quotient group G/Z(G), where Z(G) is the group center of G, is the trivial group.

The closed ball with center x and radius r is defined by B_r(x)={y:|y-x|<=r}.

A perspective collineation in which the center and axis are incident.

A line that passes through the center of a circle or sphere.

The locus of the similitude center of two circles.

In a given triangle DeltaABC with all angles less than 120 degrees (2pi/3, the first Fermat point X or F_1 (sometimes simply called "the Fermat point," Torricelli point, or ...

The triangle T that is externally tangent to the excircles and forms their triangular hull is called the extangents triangle (Kimberling 1998, p. 162). It is homothetic to ...

The combination of a central dilation and a rotation about the same center. However, the combination of a central dilation and a rotation whose centers are distinct is also a ...

The intersection H of the three altitudes AH_A, BH_B, and CH_C of a triangle is called the orthocenter. The name was invented by Besant and Ferrers in 1865 while walking on a ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...