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The points of tangency t_1 and t_2 for the four lines tangent to two circles with centers x_1 and x_2 and radii r_1 and r_2 are given by solving the simultaneous equations ...

The Miquel point is the point of concurrence of the Miquel circles. It is therefore the radical center of these circles. Let the points defining the Miquel circles be ...

If a Steiner chain is formed from one starting circle, then a Steiner chain is formed from any other starting circle. In other words, given two circles with one interior to ...

A circle with an arrow indicating a direction.

Not concentric.

The radius of the smallest circle centered at one of the points of an N-cluster, which contains all the points in the N-cluster.

The circumcircle of an ellipse, i.e., the circle whose center concurs with that of the ellipse and whose radius is equal to the ellipse's semimajor axis.

A triangle ABC formed by three circular arcs. By extending the arcs into complete circles, the points of intersection A^', B^', and C^' are obtained. This gives the three ...

Two geometric figures are said to be concentric if their centers coincide. The region between two concentric circles is called an annulus. The following table summarizes some ...

The triangulation point Y of a reference triangle DeltaABC for which triangles DeltaBYC, DeltaCYA, and DeltaAYB have congruent incircles. It is a special case of an Elkies ...