Circle Theorems

• What does the alternate segment theorem state?

  The angle between a tangent and a chord equals the angle subtended by the same chord in the alternate segment.
• How does the angle at the center theorem relate to angles at the circumference?

  The angle at the center is twice the angle at the circumference.
• What is true about angles in the same segment of a circle?

  Angles in the same segment are equal.
• What is the measure of the angle in a semicircle?

  90 degrees.
• What does the perpendicular from the center of a circle to a chord do?

  It bisects the chord into two equal parts.
• What is the relationship between opposite angles in a cyclic quadrilateral?

  They total 180 degrees.
• What is the angle between a tangent and a radius at the point of contact?

  90 degrees.
• What can be said about tangents that meet at the same point?

  Tangents which meet at the same point are equal in length.
• What are the key circle theorems covered in this material?

  • Alternate segment theorem
  • Angles in the same segment theorem
  • Angle at the center theorem
  • Angles in a semicircle
  • Chord of a circle theorem
  • Tangent of a circle theorem
  • Cyclic quadrilateral theorem