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The Napoleon crossdifference is the crossdifference of the Napoleon points. It has triangle center function alpha_(1510)=((b^2-c^2)[2cos(2A)-1])/a and is Kimberling center ...

In any triangle, the locus of a point whose pedal triangle has a constant Brocard angle and is described in a given direction is a circle of the Schoute coaxal system.

Given a reference triangle DeltaABC, the trilinear vertex matrix of another triangle DeltaA^'B^'C^' is the 3×3 matrix whose rows are the trilinear coordinates of the vertices ...

The Yff contact circle is the circumcircle of the Yff contact triangle. Its center has triangle center function alpha=((b-c)(3a^3+b^3+c^3-2a^2b-2a^2c-abc))/a, (1) which does ...

Given a triangle, extend two sides in the direction opposite their common vertex. The circle tangent to these two lines and to the other side of the triangle is called an ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

The Gibert point can be defined as follows. Given a reference triangle DeltaABC, reflect the point X_(1157) (which is the inverse point of the Kosnita point in the ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...

The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle DeltaABC. It is also the center of the excircles ...

While the pedal point, Cevian point, and even pedal-Cevian point are commonly used concepts in triangle geometry, there seems to be no established term to describe the ...