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The lengths of the tangents from a point P to a conic C are proportional to the cube roots of the radii of curvature of C at the corresponding points of contact.

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.

If a line L is the Simson line of a point P on the circumcircle of a triangle, then P is called the pole of L (Honsberger 1995, p. 128).

The radial curve of the deltoid x = 1/3a[2cost+cos(2t)] (1) y = 1/3a[2sint-sin(2t)] (2) with radiant point (x_0,y_0) is the trifolium x_r = x_0+4/3a[cost-cos(2t)] (3) y_r = ...

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 ...

A fixed point for which the stability matrix has equal negative eigenvalues.

A fixed point for which the stability matrix has equal positive eigenvalues.

An origami configuration that can be pressed to a plane figure without crumpling it or adding new creases.

The Jerabek hyperbola is a circumconic that is the isogonal conjugate of the Euler line (Kimberling 1998, p. 237). Since it is a circumconic passing through the orthocenter, ...