Circle theorems

• When a cord meets a tangent it creates an angle, in that segment. This angle is equal to the angle in the alternate segment.

  
• The angle at the centre is twice the size the angle at the circumference.

  
• Angles in the same segment are equal.

  
• The angle in a semicircle is 90 degrees.

  
• Opposite angles of a cyclic quadrilateral add up to 180 degrees.

  { angle A + angle C = 180}

  { angle D + angle B = 180}

  
• Two tangents drawn from the same point outside the circle. And where they touch the circle, the tangents while be equal in length.

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