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The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

The locus of the similitude center of two circles.

The MacBeath circle, a term coined here for the first time, is the circumcircle of the MacBeath triangle. It has a fairly complicated radius, center function, and circle ...

A unit circle is a circle of unit radius, i.e., of radius 1. The unit circle plays a significant role in a number of different areas of mathematics. For example, the ...

Two knots are pass equivalent if there exists a sequence of pass moves taking one to the other. Every knot is either pass equivalent to the unknot or trefoil knot. These two ...

A great circle is a section of a sphere that contains a diameter of the sphere (Kern and Bland 1948, p. 87). Sections of the sphere that do not contain a diameter are called ...

The Bevan circle, sometimes also called the excentral circle, is the circumcircle of the excentral triangle of the reference triangle, i.e., it is the circle passing through ...

The first de Villiers point is the perspector of the reference triangle and its BCI triangle, which is Kimberling center X_(1127) and has triangle center function ...

In a given circle, find an isosceles triangle whose legs pass through two given points inside the circle. This can be restated as: from two points in the plane of a circle, ...

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.