circle theorems

• Alternate segment theorem

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

  
• Angles at centre/circumference

  the angle at the centre is double the angle at the circumference.

  
• Angles in same segment

  angles in the same segment are equal.

  
• What is a cyclic quadrilateral?

  A cyclic quadrilateral is a quadrilateral drawn inside a circle. Every corner of the quadrilateral must touch the circumference of the circle.
• Cyclic quadrilateral angles

  The opposite angles in a cyclic quadrilateral add up to 180°.

  
• Angles in a semicircle

  The angle in a semicircle is a right angle.

  
• Tangent and radius

  The angle between a tangent and a radius is 90°.

  
• Tangents meet at same point

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

  
• Chord intersect

  A chord and tangent make a 90 degree angle