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An (infinite) line determined by two points (x_1,y_1) and (x_2,y_2) may intersect a circle of radius r and center (0, 0) in two imaginary points (left figure), a degenerate ...

The radial curve of a unit circle from a radial point (x,y) and parametric equations x = cost (1) y = sint (2) is another circle with parametric equations x_r = x-cost (3) ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...

The Gergonne point Ge is the perspector of a triangle DeltaABC and its contact triangle DeltaT_AT_BT_C. It has equivalent triangle center functions alpha = [a(b+c-a)]^(-1) ...

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

The minimal enclosing circle problem, sometimes also known as the bomb problem, is the problem of finding the circle of smallest radius that contains a given set of points in ...

A pivot point of a curve is a fixed point Q such that points P lying on the curve and their (isogonal, isotomic, etc.) conjugates are collinear with Q.

The fixed point with respect to which a pedal curve or pedal triangle is drawn.

A the (first, or internal) Kenmotu point, also called the congruent squares point, is the triangle center constructed by inscribing three equal squares such that each square ...

Let DeltaABC be a triangle and D a point on the side BC. Let I be the incenter, P the center of the circle tangent to the circumcircle and segments AD and BD, Q the center of ...