In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the center. Circles are simple closed curves which divide the plane into an interior and exterior. The circumference of a circle is the perimeter of the circle, and the interior of the circle is called a disk. An arc is any continuous portion of a circle. A circle is a special ellipse in which the two foci coincide (i.e., are the same point). Circles are conic sections attained when a right circular cone is intersected with a plane perpendicular to the axis of the cone. Analytic results In an x-y coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that left( x - a right)^2 + left( y - b right)^2=r^2.

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