Circle theorems

• The angle subtended by an arc at the centre is twice the angle subtended at the circumference

  
• The angles at the circumference subtended by the same arc are equal

  
• Opposite angles in a cyclic quadrilateral add to 180

  
• The angle at the circumference in a semicircle is a right angle 


  P = right angle

  
• 1. The angle between a tangent and a radius is 90

  
• Tangents which meet at the same point are equal in length

  
• The perpendicular from the centre of the chord bisects the chord

  
• The angle between a tangent and a chord is equal to the angle in the alternate segment