Circle Theorems

• Alternate segment theorem


  The angle that lies between a tangent and a chord = to the angle subtended by the same chord in the alternate segment

  
• Angle at the circle theorem


  The angle at the centre is twice the angle at the circumference

  
• Angles in the same segment theorem

  Angles in the same segment are equal

  
• Angles in a semicircle


  The angle in a semicircle is 90 degrees

  
• Chord of a circle


  The perpendicular from the centre of a circle to a chord bisects the chord (splits chord into two equal parts)

  
• Cyclic quadrilateral


  The opposite angles in a cyclic quadrilateral total 180 degrees.

  
• Tangent of a circle

  A: The angle between a tangent and radius is 90 degrees.

  B: Tangents which meet at the same point are equal in length