Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Problem solving with circle theorems

      Lesson details

      Learning outcome

      I can use my knowledge of circle theorems to solve problems.

      Key learning points

      1. Circle theorems can be used in situations involving circles
      2. It is not always obvious that a circle theorem can be used
      3. Sometimes you may wish to add more to a diagram in order to deduce more information

      Keywords

      • Tangent - A tangent of a circle is a line that intersects the circle exactly once.

      • Chord - A chord is any line segment joining two points on the circumference of a circle.

      • Perpendicular - Two lines are perpendicular if they meet at right angles.

      • Equidistant - Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.

      Common misconception

      Pupils may not recognise or confuse which circle theorems to apply in a multi-step problem.

      Encourage pupils to add more to a diagram in order to deduce more information about the problem. Drawing an additional line segment, such chord or radius may a useful first step.

      Teacher tip

      For some questions, different combinations of circle theorems can be applied to solve the problem. Encourage pupils to write down which circle theorem they are using at each stage of their solution and discuss the efficiency of alternate solutions.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      $$a$$° = °.

      An image in a quiz
      Correct Answer: 54, 54°, 54 degrees

      Q2.
      Calculate the size of angle $$b$$°.

      An image in a quiz
      27°
      36°
      54°
      Correct answer: 108°
      126°

      Q3.
      The diagram shows a circle with a tangent and three line segments that form a triangle inside the triangle. $$c$$° = °.

      An image in a quiz
      Correct Answer: 108, 108°, 108 degrees

      Q4.
      $$d$$° = °.

      An image in a quiz
      Correct Answer: 96, 96°, 96 degrees

      Q5.
      Points A and B are points where two separate tangents intersect the circle. $$c$$° = °.

      An image in a quiz
      Correct Answer: 47, 47°, 47 degrees

      Q6.
      Points A and B are points where two separate tangents intersect the circle. Find the size of angle $$d$$°.

      An image in a quiz
      Correct answer: 38°
      42°
      43°
      47°

      6 Questions

      Q1.
      The length of chord MN is cm (2 d.p.).

      An image in a quiz
      Correct Answer: 29.66, 29.66 cm

      Q2.
      $$a$$° = ° (2 d.p.).

      An image in a quiz
      Correct Answer: 67.98, 67.98 degrees, 67.98°

      Q3.
      $$u = 7k + 4$$. $$v = 9k$$. $$u$$° = °.

      An image in a quiz
      Correct Answer: 81, 81°, 81 degrees

      Q4.
      $$m + k = 207$$. $$k$$° = °.

      An image in a quiz
      Correct Answer: 138, 138°, 138 degrees

      Q5.
      The image shows a circle, a tangent to the circle and a number of chords and radii within the circle. $$b : c : d = 5 : 7 : 6$$. $$e$$° = °.

      An image in a quiz
      Correct Answer: 35, 35°, 35 degrees

      Q6.
      The image shows a circle, a tangent to the circle and a number of chords and radii within the circle. $$b : c : d = 5 : 7 : 6$$. $$g : h = 14 : 9$$. $$h$$° = °.

      An image in a quiz
      Correct Answer: 63, 63°, 63 degrees

      To help you plan your 10 maths lesson on: Problem solving with circle theorems, download all teaching resources for free and adapt to suit your pupils' needs...