Grade 11 Maths · Euclidean Geometry

Use angles of a cyclic quadrilateral

Use the fact that opposite angles of a quadrilateral inside a circle add up to 180°, for example if one is 70°, the opposite one is 110°.

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Circle Geometry Grade 11 : Cyclic QuadrilateralKevinmathscience

Circle Geometry Grade 11 Cyclic Quadrilaterals: Opposite angles cyclic quadsMiss Martins Maths and Science

Circle Geometry Grade 11 Cyclic Quadrilaterals: Exterior Angle Cyclic QuadMiss Martins Maths and Science

Circle Geometry Grade 11 : Cyclic Quadrilateral PracticeKevinmathscience

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Question 8.3 · March 2021 · Provincial · 2 marks

In the figure, RDS is a tangent to circle O at D.

BC = D C

, and

C \hat{D} S = 4 0^{\circ}

. Calculate the size of the following angles, with reasons. Diagram for this question

8.3

\hat{A}

(2)

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

More past paper questions: use angles of a cyclic quadrilateral

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3. Question 4.2.4 · 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:
4.2.4 $\hat{E}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{E} = 18 0^{\circ} - 2 5^{\circ} = 15 5^{\circ}$
  1 mark · Use angles of a cyclic quadrilateral
2. ✓
  Ropp $∠$ s of cyclic quad ( $A BEC$ )
  1 mark · Use angles of a cyclic quadrilateral
4. Question 5.2.1(d) · 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(d) $A \hat{E} D$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Statement $A \hat{E} D = 18 0^{\circ} - 7 2^{\circ} = 10 8^{\circ}$
  1 mark · Use angles of a cyclic quadrilateral
2. ✓
  Reason(opposite angles of cyclic quad $A B D E$ )
  1 mark · Use angles of a cyclic quadrilateral
5. Question 9.2.2 · 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: $Diagram for question 9.2$
9.2.2 $\hat{Q}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S $\hat{Q} = 180° - 115° = 65°$
  1 mark · Use angles of a cyclic quadrilateral
2. ✓
  R[opposite $∠$ s of cyclic quad]
  1 mark · Use angles of a cyclic quadrilateral
6. Question 4.3.1(c) · 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(c) Determine $\hat{D}$ (2)
Show the memo (2 ticks)Memo
1. ✓
  S: $\hat{D} = 11 5^{\circ}$ $\hat{D} = 18 0^{\circ} - 6 5^{\circ} = 11 5^{\circ}$
  1 mark · Use angles of a cyclic quadrilateral
2. ✓
  R: opposite angles of a cyclic quadrilateral[opp. $∠$ s of a cyclic quadrilateral]
  1 mark · Use angles of a cyclic quadrilateral

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