Grade 11 Maths · Euclidean Geometry · Use equal chords, equal angles

Use equal chords, equal angles Grade 11

Use the fact that equal chords subtend equal angles at the circumference or at the centre, and the converse, for example AB = CD gives the angles standing on AB and CD equal.

questions use it, all grades · 7 past paper, 13 practice: 20 questions use it, all grades · 7 past paper, 13 practice

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Question 10.3 · November 2017 · Paper 2 · National (DBE) · 3 marks

M is the centre of the circle SVQR having equal chords SV and QR.
RP and QP are tangents to the circle at R and Q respectively such that R

\hat{P}

= 70°

. $Diagram for this question$

10.3 Determine the size of

\hat{M}_{2}

.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: use equal chords, equal angles

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3. Question 9.1.2 · November 2018 · Paper 2 · National (DBE) · 2 marks
Give reasons for your statements and calculations in QUESTIONS 9, 10 and 11.
9.1 In the figure, O is the centre of the circle. A, B, C, D and E lie on the circle such that chord AB and chord DC are equal in length and $\hat{A EB} = 39°$ .

Answer the questions that follow. $Diagram for question 9.1$
9.1.2 Determine the size of $\hat{O}_{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{O}_{2} = 78°$
  1 mark · Use equal chords, equal angles
2. ✓
  R[equal chords; equal $∠$ s]
  1 mark · Use equal chords, equal angles
4. Question 9.2.2 · November 2016 · Paper 2 · National (DBE) · 2 marks
Give reasons for your statements and calculations in QUESTIONS 9, 10, 11 and 12.
9.2 O is the centre of circle TNSPR. $P \hat{O} S = 60°$ and $PS = NT$ .

Calculate the size of: $Diagram for question 9.2$
9.2.2 $N \hat{S} T$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $N \hat{S} T = 30°$
  1 mark · Use equal chords, equal angles
2. ✓
  R[equal chords subtend equal angles]
  1 mark · Use equal chords, equal angles
5. Question 9.2.2 · September 2024 · Paper 2 · Provincial · 2 marks
9.2 PT is a tangent to the circle at T. PR $∥$ TS and PQR is a straight line. Q, R and S are points on the circumference of the circle. $\hat{R}_{2} = y$ and $\hat{S} = x$ . QR $=$ TS.

Answer the questions that follow. $Diagram for question 9.2$
9.2.2 Determine, giving reason, another angle which is equal to $\hat{T}_{2}$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{T}_{2} = \hat{R}_{1}$
  1 mark · Use equal chords, equal angles
2. ✓
  R[ $∠$ s subt by equal chords]
  1 mark · Use equal chords, equal angles
6. Question 8.2 · September 2026 · Paper 2 · Provincial · 3 marks
GIVE REASONS FOR YOUR STATEMENTS IN QUESTIONS 8, 9 AND 10.

In the diagram below, points A, B, C and D lie on the circumference of a circle with $BC ∥ A D$ . CB is produced to E and DG is a tangent to the circle at D. $A D = B D$ and $E \hat{B} A = 67°$ . $Diagram for this question$
8.2 Prove, giving reasons, that $A B = C D$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  METHOD 1: S $\hat{D}_{2} = \hat{B}_{3}$
  1 mark · Use angles on parallel lines
2. ✓
  METHOD 1: R[alt $∠$ s; BC $∥$ AD]
  1 mark · Use angles on parallel lines
3. ✓
  METHOD 1: R $∴ A B = C D$ [converse: equal chords subtend equal angles]
  1 mark · Use equal chords, equal angles

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