Circle Theorems

• What are circle theorems used for?

  Geometric proofs and calculating angles
• What is a theorem in mathematics?

  • A mathematical statement
  • Can be demonstrated to be true
• How many circle theorems are there?

  Seven
• What does the term 'subtend' mean in circle theorems?

  To create an angle at a given point
• What is a chord in a circle?

  A straight line joining two points on a circle
• What is the arc in a circle?

  The curve between two points on the circumference
• What is the relationship between chords and angles in circle theorems?

  An angle is subtended by the arc between two chords
• What is the significance of angles at the center and circumference in circle theorems?

  They help define relationships between angles
• How do circle theorems assist in geometric proofs?

  By providing established relationships between angles
• How do circle theorems relate to cyclic quadrilaterals?

  Cyclic quadrilaterals have angles defined by circle theorems
• If two chords intersect inside a circle, what can be inferred about the angles formed?

  The angles are related by circle theorems
• What are the key properties of angles in a semicircle?

  • Angles in a semicircle are right angles
  • They subtend the diameter of the circle
• What is the alternate segment theorem?

  • Relates angles formed by tangents and chords
  • States that the angle in the alternate segment is equal
• How can circle theorems be used to solve problems?

  • By applying relationships between angles
  • Using properties of chords and arcs