The MathResource
circle,
n. 1a. a closed plane curve every point of which is equidistant from a given fixed point, the center. Its equation is
Maple Image,
where r is the radius, and (h, k) is the center; its parametric equations are
x = r cos θ; y = r sin θ
(compare ellipse). It has circumference of length 2πr.
b. the figure enclosed by such a curve, with area πr2. The figure below shows such a figure together with some of its more important elements.

2. see great circle. 3. (Logic) see vicious circle.