The center of something is generally its middle. In the context of geometry, the center is the point in the middle of an object.

Center of a circle

The center of a circle is a point inside a circle that is equal in distance from all of the points on the circle.

Points A, B, C, and D are equidistant from point O in the circle above, as is any point that lies on the circle. A radius is a line segment that has one endpoint on the center of the circle and the other endpoint on the circle's circumference. A circle has infinitely many radii (plural for radius), and each radius has an equal measure.

The diameter of a circle is a chord that passes through the circle's center.

Diameter AB shown for the circle above. The diameter of a circle can be broken into two radii.

Concentric circles are a set of circles that have the same center.

The three circles above share their center.

Constructing the center of a circle

You can construct the center of a given circle with a compass and straightedge. Follow these steps:

  1. Draw 2 non-parallel chords AB and CD.
  2. Draw the perpendicular bisectors of the chords. The intersection of the two perpendicular bisectors, O, is the center of the circle.

Center of a circle in coordinate geometry

In coordinate geometry, a circle can be expressed as (x-h)2 + (y-k)2 = r2. The center of the circle with radius r in this equation is located at point (h, k).


Find the center of the circle given in general form.

x2 + 4x + y2 - 2y - 11 = 0

The equation above can be rearranged as:

(x2 + 4x + 4) + (y2 - 2y + 1) = 16

(x+2)2 + (y-1)2 = 42

So, the circle has a radius of 4 units and its center is at (-2, 1). The graph of the circle is shown below.

Center of a polygon

The center of a regular polygon is the same as the center of its circumscribed circle. The center is equidistant from all its vertices.

The regular pentagon shares the same center as circle A.

Center of a sphere

The center of a sphere is a point inside a sphere that is equidistant from all points that form the sphere.

In coordinate geometry, a sphere can be expressed as (x-a)2 + (y-b)2 + (z-c)2 = r2. Using this equation, the center of the sphere with radius r is located at point (a, b, c).