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The illustrations above show a number of hyperbolic tilings, including the heptagonal once related to the Klein quartic. Escher was fond of depicting hyperbolic tilings, ...

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 points of tangency of the Lucas inner circle with the Lucas circles are the inverses of the vertices A, B, and C in the Lucas circles radical circle. These form the Lucas ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...

A spheric section is the curve formed by the intersection of a plane with a sphere. Excluding the degenerate cases of the plane tangent to the sphere or the plane not ...

A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a ...

The center of the Taylor circle. It has triangle center function alpha_(389)=cosA-cos(2A)cos(B-C) and is Kimberling center X_(389), which is the center of the Spieker circle ...

The Yiu A-circle of a reference triangle DeltaABC is the circle passing through vertex A and the reflections of vertices B and C with respect to the opposite sides. The Yiu ...

The locus of the point at which two given circles possess the same circle power is a straight line perpendicular to the line joining the midpoints of the circle and is known ...