Circle theorems: past paper questions

Where the questions come from

• Question 9May/June 2026, paper 13Structured5 marksHas a diagram

  $A$, $B$ and $C$ are points on the circumference of the circle, centre $O$. $DAE$ is a tangent to the circle at $A$. $DE$ is parallel to $BC$.

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• Question 24Oct/Nov 2025, paper 12Structured1 mark

  $B$ is a point on the circle, centre $O$. $ABC$ is a tangent to the circle at $B$ and angle $OAB={36}^{\circ }$. Work out the size of angle $AOB$.

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• Question 7Oct/Nov 2024, paper 33Structured12 marksHas a diagram

  Write down the mathematical name for this solid.

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• Question 17Oct/Nov 2023, paper 12Structured4 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle, centre $O$. Draw a tangent to the circle at point $A$.

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• Question 19May/June 2026, paper 31Structured3 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on the circumference of a circle with centre $O$. $AB=AD$ and angle $BDC={52}^{\circ }$. $BD$ is a diameter of the circle.

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• Question 20Oct/Nov 2025, paper 31Structured4 marksHas a diagram

  Work out the size of one interior angle of a regular 8-sided polygon.

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• Question 5May/June 2024, paper 32Structured12 marksHas a diagram

  The diagram shows a pair of parallel lines and a straight line. Write down the mathematical name for the type of angle marked ${125}^{\circ }$.

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• Question 20May/June 2023, paper 13Structured3 marksHas a diagram

  The diagram shows a circle, centre $O$, diameter $AB$. $A$, $B$ and $C$ lie on the circumference of the circle. Write down the mathematical name of the line $AC$.

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• Question 25May/June 2026, paper 33Structured5 marksHas a diagram

  The diagram shows a circle, centre $O$ and diameter $AC$. $B$ is a point on the circumference of the circle. Give the geometrical reason why angle $ABC={90}^{\circ }$.

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• Question 21May/June 2025, paper 11Structured2 marksHas a diagram

  Points $A$, $B$ and $C$ lie on the circle, centre $O$. Work out angle $BCA$.

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• Question 5May/June 2024, paper 33Structured11 marksHas a diagram

  Measure angle $k$.

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• Question 7May/June 2023, paper 31Structured14 marksHas a diagram

  The diagram shows a circle, centre $O$, with points $B$, $D$ and $E$ on the circumference. $AOEF$ is a straight line. The straight line $AC$ touches the circle at $B$.

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• Question 18May/June 2025, paper 13Structured5 marksHas a diagram

  The diagram shows a circle, centre $O$. $P$ and $S$ are points on the circle. $POR$ is a straight line.

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• Question 10May/June 2025, paper 32Structured5 marksHas a diagram

  A, B and C are points on a circle, centre O, diameter AC. Complete these statements, giving geometrical reasons.

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• Question 18May/June 2025, paper 33Structured2 marksHas a diagram

  Points $C$ and $D$ lie on the circle. Write down the mathematical name for the line $CD$.

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