EDEXCEL GCSE Maths

• What is a circle defined as?

  A set of points equidistant from a center
• What is the definition of a radius?

  A line from the center to the circumference
• What is a chord in a circle?

  A line connecting two points on the circumference
• What is a tangent?

  A line that touches a circle at one point
• What is an arc?

  Part of the circumference of a circle
• What is a cyclic quadrilateral?

  A four-sided shape with vertices on a circle
• What does Theorem 1 state about angles at the center and circumference?

  The angle at the center is twice the circumference angle
• How can you prove Theorem 1 about angles at the center and circumference?

  By drawing a radius to the circumference angle
• What is the significance of Theorem 1 in circle geometry?

  It helps find unknown angles in circles
• What does Theorem 2 state about angles in a semi-circle?

  Angles in a semi-circle are 90°
• How is Theorem 2 related to Theorem 1?

  It is a special case where the center angle is 180°
• What does Theorem 3 state about angles in the same segment?

  Angles in the same segment are equal
• Why are angles in the same segment equal according to Theorem 3?

  They subtend the same arc at the circumference
• What does Theorem 4 state about opposite angles in cyclic quadrilaterals?

  Opposite angles sum to 180°
• How can you prove Theorem 4 about opposite angles?

  Each pair of opposite angles is supplementary
• What does Theorem 5 state about the radius and tangent?

  The radius is perpendicular to the tangent at contact
• Why must the radius be perpendicular to the tangent according to Theorem 5?

  Otherwise, a shorter line could be drawn
• What does Theorem 6 state about tangents from an external point?

  The tangents are equal in length
• Why are the angles between each tangent and the line to the center equal?

  Because the triangles formed are congruent
• What should you do when solving problems involving circle theorems?

  Label all given information clearly
• What are the steps to apply circle theorems in problem-solving?

  • Label all given information clearly
  • Identify useful theorem(s)
  • Apply theorems step by step
  • State reasons for each step
  • Check if the answer is reasonable
• How can circle theorems be combined?

  • Use multiple theorems for complex problems
  • Always state which theorem is used