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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 ...

A self-isogonal cubic us a triangle cubic that is invariant under isogonal conjugation. The term is commonly applied to mean a pivotal isogonal cubic, in which points P lying ...

A self-isotomic cubic us a triangle cubic that is invariant under isotomic conjugation. The term is commonly applied to mean a pivotal isotomic cubic, in which points P lying ...

The Simson cubic is the triangle cubic that is the locus of tripoles of the Simson lines of a triangle DeltaABC. It has trilinear equation ...

Consider two directly similar triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 with B_1C_1:A_1C_1:A_1B_1=B_2C_2:A_2C_2:A_2B_2=a:b:c. Then a·A_1A_2, b·B_1B_2 and c·C_1C_2 form the ...

The Yiu A-circle of a reference triangle DeltaABC is the circle passing through vertex A and the reflections of vertices B and C with respect to the opposite sides. The Yiu ...

Geometry

Trigonometry

The point of concurrence of the four maltitudes of a cyclic quadrilateral. Let M_(AC) and M_(BD) be the midpoints of the diagonals of a cyclic quadrilateral ABCD, and let P ...

Given two bicentric points P=p:q:r and U=u:v:w, their bicentric sum is defined by p+u:q+v:r:w.