Circle theorems II: past paper questions

Where the questions come from

• Question 15May/June 2026, paper 22Structured5 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle. $EF$ is a tangent to the circle at $A$. Angle $ADB={20}^{\circ }$ and angle $BCD={75}^{\circ }$.

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• Question 12Oct/Nov 2025, paper 42Structured4 marksHas a diagram

  $A$, $B$ and $C$ lie on a circle centre $O$. $DE$ is a tangent to the circle at $C$. Angle $ABC={52}^{\circ }$ and angle $BCE={65}^{\circ }$.

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• Question 14Oct/Nov 2024, paper 23Structured4 marksHas a diagram

  $A,B,C$ and $D$ lie on the circle. $TAS$ is a tangent to the circle at $A$. Find the value of $x$.

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• Question 17Oct/Nov 2023, paper 21Structured3 marksHas a diagram

  $A$, $B$ and $C$ are points on the circumference of a circle, centre $O$. Tangent $DE$ touches the circle at $C$. Angle $BCE={53}^{\circ }$ and angle $ACO={20}^{\circ }$.

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• Question 10May/June 2025, paper 21Structured4 marksHas a diagram

  $A$, $B$ and $C$ are three points on a circle, centre $O$. $DE$ is a tangent to the circle at $A$. Angle $ACO={35}^{\circ }$ and angle $BCO={40}^{\circ }$.

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• Question 14May/June 2024, paper 23Structured3 marksHas a diagram

  $P$, $Q$, $R$ and $T$ are points on the circle. $AB$ is a tangent to the circle at $T$. Angle $ATP={50}^{\circ }$, angle $PTR={48}^{\circ }$ and $PQ=QR$.

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• Question 17Oct/Nov 2023, paper 22Structured4 marksHas a diagram

  $A$, $B$ and $C$ are points on a circle, centre $O$. Angle $OBA={28}^{\circ }$. Find angle $ACB$.

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• Question 2May/June 2024, paper 42Structured9 marksHas a diagram

  The diagram shows a straight line intersecting two parallel lines. Find the value of $a$ and the value of $b$.

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