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Let a circle C_1 lie inside another circle C_2. From any point on C_2, draw a tangent to C_1 and extend it to C_2. From the point, draw another tangent, etc. For n tangents, ...

The reciprocal curve of a given circle is the locus of a point which moves so that its distance from the center of reciprocation varies as its distance from the line which is ...

The circumcircle, Brocard circle, Lemoine axis, and isodynamic points belong to a coaxal system orthogonal to the Apollonius circles, called the Schoute coaxal system. In ...

Draw an initial circle, and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite ...

A straight line is tangent to a given curve f(x) at a point x_0 on the curve if the line passes through the point (x_0,f(x_0)) on the curve and has slope f^'(x_0), where ...

A tube of radius r of a set gamma is the set of points at a distance r from gamma. In particular, if gamma(t) is a regular space curve whose curvature does not vanish, then ...

The curve given by the polar equation r=a(1-costheta), (1) sometimes also written r=2b(1-costheta), (2) where b=a/2. The cardioid has Cartesian equation ...

The Neuberg A_1-circle is the locus of the polygon vertex A_1 of a triangle on a given base A_2A_3 and with a given Brocard angle omega. From the center N_1, the base A_2A_3 ...

The nine-point center N (sometimes instead denoted F) is the center of the nine-point circle. It has equivalent triangle center functions alpha_5 = cos(B-C) (1) alpha_5 = ...

Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...