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The Atzema spiral, also known as the Pritch-Atzema spiral, is the curve whose catacaustic for a radiant point at the origin is a circle, as illustrated above. It has ...

The bend of a circle C mutually tangent to three other circles is defined as the signed curvature of C. If the contacts are all external, the signs of the bends of all four ...

While some authors define "circumference" as distance around an arbitrary closed object (sometimes restricted to a closed curved object), in the work, the term "perimeter" is ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

When a point P moves along a line through the circumcenter of a given triangle Delta, the pedal circle of P with respect to Delta passes through a fixed point (the Griffiths ...

If P is any point on a line TT^' whose orthopole is S, then the circle power of S with respect to the pedal circle of P is a constant (Gallatly 1913, p. 51).

Given the center of a circle, divide the circle into four equal arcs using a compass alone (a Mascheroni construction).

The power circles of a reference triangle are the three circles centered at the midpoints M_A, M_B, M_C of the sides of a reference triangle DeltaABC that pass through the ...

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 ...

Four or more points P_1, P_2, P_3, P_4, ... which lie on a circle C are said to be concyclic. Three points are trivially concyclic since three noncollinear points determine a ...