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      The perpendicular from the centre of a circle to a chord bisects the chord

      Lesson details

      Learning outcome

      I can derive and use the theorem: the perpendicular from the centre of a circle to a chord bisects the chord.

      Key learning points

      1. A theorem is a statement that can be demonstrated to be true by accepted mathematical operations and arguments
      2. Theorems can be thought of as puzzles to solve, you are showing how to find a result
      3. In order to use this theorem, you may need to draw a diagram or add more information to an existing one

      Keywords

      • Bisect - To bisect means to cut or divide an object into two equal parts.

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

      Common misconception

      Pupils may assume that a radius which intersects a chord always bisects the chord.

      A radius only bisects a chord if they are perpendicular.

      Teacher tip

      The lesson demonstrates how this circle theorem could be explored practically by using a pair of compasses, using a circular geoboard and using dynamic geometry software. Pupils may wish to explore these further for themselves.

      Equipment

      Ruler, protractor, pair of compasses, pencil

      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

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Which of these statements are correct?

      A chord can be a radius.
      Correct answer: A chord can be a diameter.
      A chord can be a tangent.
      Correct answer: A segment can be a sector.
      A minor sector can be a segment.

      Q2.
      Find the size of angle $$a$$°.

      An image in a quiz
      30°
      60°
      Correct answer: 90°
      120°
      Not enough information.

      Q3.
      The size of the angle subtended by the chord AC is °?

      An image in a quiz
      Correct Answer: 24, 24°, 24 degrees, 24degrees

      Q4.
      The image shows an 8-point geoboard. The size of angle $$b$$° is °.

      An image in a quiz
      Correct Answer: 22.5, 22.5°, 22.5 degrees

      Q5.
      On this 8-point geoboard the size of the angle labelled $$c$$° is °.

      An image in a quiz
      Correct Answer: 67.5, 67.5°, 67.5 degrees, 67.5degrees

      Q6.
      The area of triangle ABC is 336 cm². Find the area of the circle, in cm² (3 s.f.)

      An image in a quiz
      25
      48
      50
      625
      Correct answer: 1960

      6 Questions

      Q1.
      On this 10-point geoboard ∠AOM is °.

      An image in a quiz
      Correct Answer: 72, 72°, 72 degrees

      Q2.
      On this 10-point geoboard ∠OAM is °.

      An image in a quiz
      Correct Answer: 18, 18°, 18 degrees

      Q3.
      Find ∠OMA on this 10-point geoboard (in degrees).

      An image in a quiz
      Correct Answer: 90, 90°, 90 degrees

      Q4.
      BMA and OMC are straight line segments. AM = 10 cm Which of these are also 10 cm long?

      An image in a quiz
      Line segment OB
      Line segment OC
      Line segment OM
      Correct answer: Line segment BM
      Line segment CM

      Q5.
      BMA and OMC are straight line segments. AM = 10 cm. Radius OB has length 14 cm. Find the length of OM (in cm, to 2 d.p.).

      An image in a quiz
      Correct Answer: 9.80, 9.80 cm

      Q6.
      BMA and OMC are straight line segments. AM = 10 cm. Radius OB has length 14 cm. The size of ∠MOB is ° (1.d.p.).

      An image in a quiz
      Correct Answer: 45.6, 45.6°, 45.6 degrees, 45.6degrees

      To help you plan your 10 maths lesson on: The perpendicular from the centre of a circle to a chord bisects the chord, download all teaching resources for free and adapt to suit your pupils' needs...