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The de Longchamps point L is the reflection of the orthocenter H about the circumcenter O of a triangle. It has triangle center function alpha=cosA-cosBcosC, (1) and is ...

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 ...

The Longuet-Higgins point is the radical center of the circles centered at the vertices A, B, and C of a reference triangle with respective radii b+c, c+a, and a+b. It has ...

The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

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 Johnson midpoint is the point of concurrence of the line segments joining the vertices of a reference triangle with the centers of a certain set of circles (that resemble ...

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 ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

The second Steiner circle (a term coined here for the first time) is the circumcircle of the Steiner triangle DeltaS_AS_BS_C. Its center has center function ...

The center of the Taylor circle. It has triangle center function alpha_(389)=cosA-cos(2A)cos(B-C) and is Kimberling center X_(389), which is the center of the Spieker circle ...