Properties of the Circle
In geometry, a large number of facts about circles and their relations to straight lines, angles and polygons can be proved. These facts are called the properties of the circle.

Circles having equal radii are congruent.

Circles having different radii are similar.

The central angle which intercepts an arc is the double of any inscribed angle that intercepts the same arc (proof).

The radius perpendicular to a chord bisects the chord.

The chords equidistant from the center are equal in length.

A tangent to a circle is at a right angle to the radius at the point of contact.

Two tangents drawn on a circle from a point outside are equal in length.

The angle subtended at the center of a circle by its circumference is equal to four right angles.

The circumference of two different circles is proportional to their corresponding radii.

Arcs of the same circle are proportional to their corresponding angles.

Radii of the same circle or equal circles are equal.

Equal chords have equal circumferences.

The diameter of a circle is the longest chord.

Equal circles have equal circumferences.