Maths - Circle Theorems and other formulae

• Chord


  A straight line that goes from one side of the circle to the other, splitting the circle into two segments
• Angles in the same segment

  • Are equal
• Diameter


  A chord that goes straight through the center of the circle, splitting it in half
• Angle in a semicircle

  • Is 90 degrees
• Angle at the center

  • Is twice the angle at the circumference
• Cyclic quadrilateral


  A quadrilateral where all four sides touch the circumference of the circle
• Opposite angles in a cyclic quadrilateral

  • Add up to 180 degrees
• Tangent


  A straight line that touches the circle in one place
• Tangent and radius


  • Meet at 90 degrees
• Tangents from the same point


  • Are equal in length
• Tangent and chord


  • Form equal angles with each other
• Angles on a straight line add up to 180 degrees
• Angles in a triangle add up to 180 degrees