Diameter, main properties

In a circle with center $O$, a diameter is a chord that passes through $O$. The length of the diameter is $2r$, where $r$ is the radius of the circle.

Important properties

• The diameter is the longest chord in a circle.

• All diameters of a circle have the same length.

• Any chord passing through the center is a diameter.

• The diameter divides the circle into two equal semicircles.

• If $AB$ is a diameter and $C$ is any other point on the circle, then angle $ACB$ is a right angle (Thales' theorem).