Grade 11 Maths · Euclidean Geometry

Use angles in the same segment

Use the fact that angles standing on the same arc, on the same side of the chord, are equal.

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Circle Geometry Grade 11 : Angles in same segmentKevinmathscience

Circle Geometry Grade 11 Angles in same segment Euclidean Geometry Gr 11Miss Martins Maths and Science

Circle Geometry Grade 11 Angles in same segment PRACTICE Euclidean Geometry gr 11Miss Martins Maths and Science

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Question 9.2.3 · May/June 2025 · Paper 2 · National (DBE) · 4 marks

Provide reasons for your statements in QUESTIONS 9 and 10.

9.2 In the diagram, POL is a diameter of the larger circle with centre O. TMR is a diameter of the smaller circle with centre M. The two circles intersect at L and R.
PLK is a tangent to the smaller circle at L and TR is a tangent to the larger circle at R. OM intersects the smaller circle at N. Straight lines LT, LR, LN and PR are drawn.

Prove, giving reasons, that: Diagram for question 9.2

9.2.3 LN bisects

O \hat{L} R

(4)

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More past paper questions: use angles in the same segment

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3. Question 4.2.3 · June 2024 · Paper 2 · Provincial · 2 marks
4.2 In the given figure, $D \hat{C} O = 2 5^{\circ}$ , $O$ is the center of the circle. $A$ , $B$ , $E$ , $C$ and $D$ are points on the circumference. Calculate with reasons, the size of:
4.2.3 $\hat{A}_{1}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{A}_{1} = 2 5^{\circ}$
  1 mark · Use angles in the same segment
2. ✓
  R $∠$ s in same segment
  1 mark · Use angles in the same segment
4. Question 4.3.1(b) · 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(b) Determine $\hat{A}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S: $\hat{A} = 6 5^{\circ}$ $\hat{A} = \hat{B} = 6 5^{\circ}$
  1 mark · Use angles in the same segment
2. ✓
  R: angles in the same segment[ $∠$ s in the same segment]
  1 mark · Use angles in the same segment
5. Question 10.1.2(b) · November 2024 · Paper 2 · Provincial · 3 marks
10.1 In the diagram, O is the centre of circle ABP. PB is extended to C. AC is drawn. PN is a tangent to the circle at P. OC intersects AP perpendicularly at point O. $\hat{P}_{2} = 37°$

Answer the questions that follow. $Diagram for question 10.1$
10.1.2 Prove that:
10.1.2(b) OC $∥$ PN(3)
Show the memo (3 ticks)Memo
1. ✓
  METHOD 1: S $\hat{C}_{2} = \hat{A}_{1} = 37°$
  1 mark · Use angles in the same segment
2. ✓
  METHOD 1: R[ $∠$ s same seg]
  1 mark · Use angles in the same segment
3. ✓
  METHOD 1: R $∴$ OC $∥$ PN [alt. $∠$ s $=$ ]
  1 mark · Use angles on parallel lines
6. Question 9.2.3 · November 2025 · Paper 2 · Provincial · 4 marks
9.2 In the diagram below, P, Q, R and T are points on the circumference of the circle. PS is a tangent to the circle at P. Chord QR is produced to S. M and N are points on PS and RP respectively such that MN $∥$ PR. PN is drawn. QT is produced to M.

Answer the questions that follow. $Diagram for question 9.2$
9.2.3 Prove that PN bisects $S \hat{P} R$ (4)
Show the memo (4 ticks)Memo
1. ✓
  S/R $\hat{P}_{3} = \hat{N}_{2}$ [alt. $∠$ s, MN $∥$ PR]
  1 mark · Use angles on parallel lines
2. ✓
  S $\hat{N}_{2} = \hat{Q}_{1}$
  1 mark · Use angles in the same segment
3. ✓
  R[ $∠$ s same seg]
  1 mark · Use angles in the same segment
4. ✓
  S/R $\hat{Q}_{1} = \hat{P}_{4}$ [tan chord theo]
  $∴ \hat{P}_{3} = \hat{P}_{4}$
  PN bisects $S \hat{P} R$
  1 mark · Use the tan-chord theorem

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