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      Checking and securing understanding of the parts of a circle

      Lesson details

      Learning outcome

      I can identify the parts of a circle, including finding the area and perimeter of a sector.

      Key learning points

      1. A chord splits the circle into two uneven pieces
      2. The smaller piece is the minor segment and the larger is the major segment
      3. Using fractions, you can calculate the area of a sector of a circle and you can calculate the curved length of a sector
      4. To find the perimeter, you will need to add the radius twice
      5. An exact answer may be given in terms of π

      Keywords

      • Subtended - An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.

      Common misconception

      Pupils may think that every line segment that touches a circle exactly once is a tangent (even when it is not perpendicular to the radius at that point).

      If unsure, try extending the line segment to beyond the edges of the circle to check whether it would intersect the circle again.

      Teacher tip

      After recapping all the parts of a circle, pupils could practise recalling them by quizzing each other: one person describes a part of a circle (e.g. "A line segment between two points on the circumference") and the other person replies with the name of the part (e.g. "chord").

      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.
      What is the dashed line segment on this circle called?

      An image in a quiz
      arc
      chord
      circumference
      diameter
      Correct answer: radius

      Q2.
      The length of the diameter of this circle is cm.

      An image in a quiz
      Correct Answer: 13, 13 cm, thirteen

      Q3.
      The diameter of a circular fence is greater than 8 metres long. Which of these are possible lengths of the radius of this fence?

      1 metre
      π metres
      4 metres
      Correct answer: 5.5 metres
      Correct answer: 7 metres

      Q4.
      A semicircular sector has been cut from a full circle of equal radius. What fraction of the full circle is this sector?

      Correct answer: $$1\over2$$
      Correct answer: $$2\over4$$
      $$9\over10$$
      Correct answer: $$180\over360$$
      $$75\over100$$

      Q5.
      This sector has been cut from a circle. What fraction of the full circle is this sector?

      An image in a quiz
      $$1\over4$$
      Correct answer: $$1\over5$$
      $$1\over6$$
      $$72\over100$$
      Correct answer: $$72\over360$$

      Q6.
      This circular sector is broken down into two straight line segments and an arc. The perimeter of this arc is cm.

      An image in a quiz
      Correct Answer: 28, 28 cm

      6 Questions

      Q1.
      What is the dashed line segment on this circle called?

      An image in a quiz
      arc
      Correct answer: chord
      sector
      segment
      tangent

      Q2.
      What is the shaded region on this circle called?

      An image in a quiz
      arc
      sector
      Correct answer: segment
      semicircle
      tangent

      Q3.
      Which of these statements are always correct?

      A circular sector is made from exactly one radius on the circle and an arc.
      Correct answer: A circular sector is made from exactly two radii on the circle and an arc.
      A circular sector is made from exactly one chord on the circle and an arc.
      A circular sector is made from exactly two chords on the circle.
      A circular sector is made from either radii or chords on the circle and an arc.

      Q4.
      The size of the angle subtended by chord AB is degrees.

      An image in a quiz
      Correct Answer: 65, 65 degrees, 65degrees, 65°

      Q5.
      The size of the angle subtended by chord AC is degrees.

      An image in a quiz
      Correct Answer: 70, 70 degrees, 70degrees, 70°

      Q6.
      ∠XOY is a 60° angle at the centre of a circle subtended by the arc XY. The circle has a radius of 42 cm. The area of the sector OXY is cm² (2 s.f.)

      Correct Answer: 920, 920 cm², 920cm²

      To help you plan your 10 maths lesson on: Checking and securing understanding of the parts of a circle, download all teaching resources for free and adapt to suit your pupils' needs...