MATHEMATICS

• Chord


  A straight line that goes from one side of the circle to the other, splitting the circle into two segments
• Segment


  The part of the circle on one side of a chord
• First Circle Theorem

  • Angles in the same segment are equal
• The first theorem is sometimes informally referred to as the "bow tie theorem"</b>
• Second Circle Theorem

  • The angle in a semicircle is 90 degrees
• Third Circle Theorem

  • The 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
• Fourth Circle Theorem

  • The opposite angles in a cyclic quadrilateral add up to 180 degrees
• Tangent


  A straight line that touches the circle in one place
• Fifth Circle Theorem

  • A tangent meets a radius at 90 degrees
• Sixth Circle Theorem

  • Tangents from the same point are equal in length
• Seventh Circle Theorem

  • A tangent bisects the angle between the radius and the chord
• Eighth Circle Theorem

  • The angle the tangent makes with the chord is equal to the angle the chord makes at the circumference in the alternate segment