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A circle is a shape composed of all points on a plane at a given distance from a given point (Center); equivalently, it is a curve drawn by points moving in a plane, so its distance from a given point is constant. The distance from any point of the circle to the center is called the radius. Unless otherwise stated, this paper deals with the circle in Euclidean geometry, especially the Euclidean plane.

Specifically, a circle is a simple closed curve that divides a plane into two regions: interior and exterior. In daily use, the term "circle" can be used interchangeably, referring to the boundary of the figure or the whole figure (including its interior); in strict technical use, the circle is just the boundary, and the whole figure is called the disc.

A circle can also be defined as a special ellipse, in which the two focal points coincide and the eccentricity is 0, or a two-dimensional shape that uses a variation algorithm to enclose the two-dimensional shape with the most square area per unit circumference.

A circle is a plane figure defined by a line, so all right lines drawn from a point within it to the boundary line are equal. Boundary lines are called circles, and points are called centers.