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.