circle theorems

• tangent theorem

  • angle between tangent and radius is always 90 degrees

  
• two tangent theorem

  • two tangents create a kite and two congruent triangles
  • angle FGE = angle EFG

  
• chord theorem

  • a perpendicular line from the centre to a chord, bisects the chord

  
• cyclic theorem

  • opposite angles = 180 degrees
• angles in the same sector

  •  angles at the circumference subtended by the same arc are equal
  • angles in the same segment are equal

  
• double angles

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

  
• sector/diameter

  
  

  • angle at the circumference in a semicircle is a right angle
  • angle APB = 90

  
• alternate segment theorem

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