Grade 11 Maths · Euclidean Geometry

Use angle at the centre

Use the fact that the angle at the centre of a circle is twice the angle at the circumference on the same arc, for example 80° and 40°.

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Circle Geometry Grade 11 : Angle at centreKevinmathscience

Circle Geometry Grade 11 Euclidean Geometry: Angle at Centre = 2 x angle at circumferenceMiss Martins Maths and Science

Circle Geometry Grade 11 Euclidean Geometry: Angle at Centre PRACTICE QUESTIONSMiss Martins Maths and Science

Angle at the Center (Circle Theorems)StudyPass

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Question 11.1 · November 2024 · Paper 2 · Provincial · 2 marks

The circle ASBK with center O is given below. Furthermore, a semicircle is drawn through points A, O, B, T and R. P lies on AR.

A \hat{O} B = 140°

. $Diagram for this question$

11.1 Calculate the size of

\hat{S}

.(2)

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More past paper questions: use angle at the centre

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3. Question 9.2.1 · November 2024 · Paper 2 · Provincial · 2 marks
9.2 In the diagram, O is the centre of the circle with a reflex angle of 230°. P, Q, R and S are points on the circumference of the circle with chord SR extended to point T. Q $\hat{R}$ T $= 85°$ and O $\hat{P}$ S $= 20°$ .

Calculate the magnitude of the following angles: $Diagram for question 9.2$
9.2.1 $\hat{S}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{S} = 115°$
  1 mark · Use angle at the centre
2. ✓
  R[ $∠$ at the centre $= 2 \times ∠$ at the circumference]
  1 mark · Use angle at the centre
4. Question 5.2.1(c) · June 2024 · Paper 2 · Provincial · 2 marks
5.2 In the diagram below, $O$ is the centre of the circle and $A C$ is the diameter.
$A C$ is produced to meet $E D$ produced at $G$ . $OE ∥ C D$ and $\hat{B} = 7 2^{\circ}$ .
5.2.1 Calculate, giving reasons, the size of:
5.2.1(c) $\hat{D}_{4}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Statement $\hat{O}_{1} = 2 \hat{D}_{4}$ , so $\hat{D}_{4} = 3 6^{\circ}$
  1 mark · Use angle at the centre
2. ✓
  Reason(angle at centre = $2 \times$ angle at circumference)
  1 mark · Use angle at the centre
5. Question 3.3.1 · March 2022 · Provincial · 2 marks
Give reasons for your statements and calculations in Question 3.
3.3 In the diagram, O is centre of the circle. Points A, B, C and D lie on the circumference of the circle. BOD is a diameter. $\hat{A}_{1} = 5 1^{\circ}$ and $\hat{B}_{1} = 2 9^{\circ}$ . A line is drawn from O to F such that the length of BC = 24 m and radius of the circle centred O is 13 m.
3.3.1 Determine the size of $C \hat{O} B$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Statement $C \hat{O} B = 2 (5 1^{\circ}) = 10 2^{\circ}$
  1 mark · Use angle at the centre
2. ✓
  Reason $∠$ at centre $= 2 \times ∠$ at circumference
  1 mark · Use angle at the centre
6. Question 4.3.1(a) · March 2021 · Paper 1 · Provincial · 2 marks
4.3 O is centre. BE || CD and $\hat{O}_{1} = 13 0^{\circ}$ . Determine angles with reasons.
4.3.1(a) Determine $\hat{B}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S: $\hat{B} = 6 5^{\circ}$ $\hat{B} = \frac{1}{2} \hat{O}_{1} = \frac{1}{2} (13 0^{\circ}) = 6 5^{\circ}$
  1 mark · Use angle at the centre
2. ✓
  R: angle at centre[ $∠$ at centre $= 2 \times ∠$ at circumference]
  1 mark · Use angle at the centre

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