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.