GCSE Maths (AQA)

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Circle Theorem Problems

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Geometry and Measures Properties and Constructions

Circle Theorem Problems

8:20 Even More Circle Theorems
Spec G10
Previous Alternate Segment Theorem Next Faces & Surfaces
  • Circle theorems can be used to calculate unknown angles and lengths in circles
  • The angle at the circumference of a circle is half the angle at the center if they are formed by the same arc
  • The distance from a meeting point of two tangent lines to the circle is the same for both tangent lines
  • Every angle formed in a semicircle is equal to 90 degrees
  • Opposite angles in a cyclic quadrilateral add up to 180 degrees
  • Twin angles, subtended by the same arc, are equal to each other
  • The angle between a tangent line and a chord in the alternate segment of a circle is equal to any angle subtended by that chord
  • Exam questions may require the use of multiple circle theorems to solve geometric problems
  • In the given example, angle FAC can be calculated by combining multiple circle theorems
  • Angle ADB is half of angle AOB, which is 40 degrees
  • Angle ACB is the opposite angle of ADB in the cyclic quadrilateral, so it is 140 degrees
  • Angle OAC in quadrilateral OBCA is 65 degrees
  • Angle FAC is the difference between 90 degrees and 65 degrees, which is 25 degrees

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