Grade 11 Maths · Euclidean Geometry · Paper 2

Circle Terminology Grade 11

Real Circle Terminology past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 10 past paper questions
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Question 6.1 · June 2024 · Paper 2 · Provincial · 1 mark

6.1 Complete the theorem:

The tangent is ... to the radius drawn to the point of contact.(1)

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4. Question 5.2.2 · June 2024 · Paper 2 · Provincial · 3 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 $\hat{B} = 7 2^{\circ}$ .
5.2.2 Prove that $A F = F D$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Determine angles inside triangle EFD $\hat{E}_{2} = \hat{D}_{1} = 5 4^{\circ}$ (corresponding angles, $OE ∥ C D$ )
  1 mark · Use angles on parallel lines
2. ✓
  Determine angle F2In $Δ EF D$ , $\hat{F}_{2}$ is an exterior angle.
  $\hat{F}_{2} = \hat{E}_{2} + \hat{D}_{4}$ (exterior angle of a triangle is equal to the sum of interior opposite angles)
  $\hat{F}_{2} = 5 4^{\circ} + 3 6^{\circ}$
  $\hat{F}_{2} = 9 0^{\circ}$
  1 mark · Use exterior angle of a triangle
3. ✓
  Conclude proof using perpendicular from centre theoremSince $\hat{F}_{2} = 9 0^{\circ}$ , the line $OF$ (from the centre) is perpendicular to chord $A D$ .
  $∴ A F = F D$ (perpendicular from centre to chord bisects the chord)
  1 mark · Use line from centre to chord
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 9.2.1 · November 2024 · Paper 2 · Provincial · 4 marks
9.2 In the diagram below O is the center of the circle with AD = BD.
OB = 20 mm and AB = 24 mm.

Calculate the length of: $Diagram for question 9.2$
9.2.1 DE(4)
Show the memo (4 ticks)Memo
1. ✓
  S&R: OD $⊥$ ABOD $⊥$ AB [line from center to midpoint of chord]
  1 mark · Use line from centre to chord
2. ✓
  Pythagoras $O D^{2} = O B^{2} - D B^{2}$ Pythagoras
  $O D^{2} = 2 0^{2} - 1 2^{2}$
  1 mark · Use the theorem of Pythagoras
3. ✓
  $O D = 16$ $O D = 256$
  $O D = 16$
  1 mark · Use the theorem of Pythagoras
4. ✓
  Answer $∴ D E = 20 - 16$
  $= 4$ mm
  1 mark · Use the theorem of Pythagoras

Circle Terminology Grade 11 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Circle Geometry Grade 11 : Line from CenterKevinmathscience

Circle Geometry Grade 11 : Tangent Radius Theorem IntroductionKevinmathscience

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