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Proportionally cutting circles are circles that intersect the sidelines of a reference triangle DeltaABC such that length of the chords that are cut off have lengths mua, ...

Given two circles with one interior to the other, if small tangent circles can be inscribed around the region between the two circles such that the final circle is tangent to ...

The Johnson midpoint is the point of concurrence of the line segments joining the vertices of a reference triangle with the centers of a certain set of circles (that resemble ...

There are two nonintersecting circles that are tangent to all three Lucas circles. (These are therefore the Soddy circles of the Lucas central triangle.) The inner one, ...

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 system of circles obtained by multiplying each radius in a coaxal system by a constant. The Tucker circles are a coaxaloid system (Johnson 1929, p. 277).

There are four completely different definitions of the so-called Apollonius circles: 1. The set of all points whose distances from two fixed points are in a constant ratio ...

Let C_1, C_2, C_3, and C_4 be four circles of general position through a point P. Let P_(ij) be the second intersection of the circles C_i and C_j. Let C_(ijk) be the circle ...

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

Members of a coaxal system satisfy x^2+y^2+2lambdax+c=(x+lambda)^2+y^2+c-lambda^2=0 for values of lambda. Picking lambda^2=c then gives the two circles (x+/-sqrt(c))^2+y^2=0 ...