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Coaxal circles are circles whose centers are collinear and that share a common radical line. The collection of all coaxal circles is called a pencil of coaxal circles ...

Concentric circles are circles with a common center. The region between two concentric circles of different radii is called an annulus. Any two circles can be made concentric ...

The Gergonne line is Oldknow's (1996) term for the perspectrix of a contact triangle DeltaDEF and its reference triangle DeltaABC. It is determined by the Nobbs points D^', ...

A (general, asymmetric) lens is a lamina formed by the intersection of two offset disks of unequal radii such that the intersection is not empty, one disk does not completely ...

Consider a reference triangle DeltaABC and externally inscribe a square on the side BC. Now join the new vertices S_(AB) and S_(AC) of this square with the vertex A, marking ...

Given a curve C and O=(x_0,y_0) a fixed point called the pedal point, then for a point P on C, draw a line perpendicular to OP. The envelope of these lines as P describes the ...

A set of four points, one of which is the orthocenter of the other three. In an orthocentric system, each point is the orthocenter of the triangle of the other three, as ...

The radical lines of three circles are concurrent in a point known as the radical center (also called the power center). This theorem was originally demonstrated by Monge ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

The factorial n! is defined for a positive integer n as n!=n(n-1)...2·1. (1) So, for example, 4!=4·3·2·1=24. An older notation for the factorial was written (Mellin 1909; ...