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Vandeghen's (1965) name for the transformation taking points to their isotomic conjugates.

If P=p:q:r and U=u:v:w are distinct trilinear points, neither lying on a sideline of the reference triangle DeltaABC, then the crosssum of P and U is the point ...

A curve which can be turned continuously inside an equilateral triangle. There are an infinite number of delta curves, but the simplest are the circle and lens-shaped ...

The Droussent cubic is the triangle cubic with trilinear equation sum_(cyclic)(b^4+c^4-a^4-b^2c^2)aalpha(b^2beta^2-c^2gamma^2)=0. It passes through Kimberling centers X_n for ...

Given positive numbers s_a, s_b, and s_c, the Elkies point is the unique point Y in the interior of a triangle DeltaABC such that the respective inradii r_a, r_b, r_c of the ...

The excentral-hexyl ellipse is the ellipse passing through vertices of the excentral and hexyl triangles (P. Moses, pers. comm., Jan. 29, 2005). It has center at the ...

In any triangle, if one of the sides is extended, the exterior angle is greater than both the interior and opposite angles.

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

If P is any point on a line TT^' whose orthopole is S, then the circle power of S with respect to the pedal circle of P is a constant (Gallatly 1913, p. 51).

Given an acute angle in a right triangle, the opposite side is the leg of the triangle which is not incident on the angle. Lengths of opposite and adjacent sides appear ...