Circle is the locus of points equidistant from a given point, the center of the circle. The common distance from the center of the circle to its points is called radius. Thus a circle is completely defined by its center (O) and radius (R): C(O, R) = O(R) = {x: dist(O, x) = R}.
Easier explanation: A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another.