Circle theorems I: past paper questions

Where the questions come from

• Question 18May/June 2026, paper 22Structured4 marksHas a diagram

  $A$, $B$ and $C$ lie on a circle, centre $O$. $DE$ is a tangent to the circle at $A$. Angle $BAC={80}^{\circ }$ and angle $BAD={55}^{\circ }$.

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• Question 16Oct/Nov 2025, paper 11Structured6 marksHas a diagram

  Points $Q$, $R$, $S$ and $T$ lie on a circle, centre $O$. $UV$ is a tangent to the circle at $T$. $SOQV$ is a straight line.

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• Question 9Oct/Nov 2024, paper 21Structured10 marksHas a diagram

  $ABD$ is a triangle. $C$ is a point on $BD$ and $E$ is a point on $AD$. $AB$ is parallel to $EC$ and $CD=DE$.

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• Question 15Oct/Nov 2023, paper 11Structured4 marksHas a diagram

  $B$, $C$ and $D$ are points on the circle, centre $O$. $AB$ and $AC$ are tangents to the circle. Angle $BAC={38}^{\circ }$.

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• Question 14Oct/Nov 2025, paper 12Structured4 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle, centre $O$. $EF$ is a tangent to the circle at $A$. Angle $BAF={65}^{\circ }$ and angle $AOD={80}^{\circ }$.

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• Question 16May/June 2024, paper 11Structured5 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on the circumference of a circle centre $O$. Angle $BCD={58}^{\circ }$ and angle $DBC={72}^{\circ }$. Complete the statement below.

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• Question 2Oct/Nov 2023, paper 22Structured8 marksHas a diagram

  Find the size of one interior angle of a regular 15-sided polygon.

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• Question 14May/June 2025, paper 22Structured3 marksHas a diagram

  $PQRS$ is a cyclic quadrilateral. $APB$ is a tangent to the circle at $P$. Angle $SPB={37}^{\circ }$ and angle $PSQ={85}^{\circ }$.

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• Question 17May/June 2024, paper 12Structured4 marksHas a diagram

  $A$, $B$, $C$ and $D$ are points on a circle, centre $O$. Angle $BAD={120}^{\circ }$ and angle $OBC={20}^{\circ }$. Find the value of $x$.

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• Question 3May/June 2023, paper 22Structured8 marksHas a diagram

  The diagram shows the equilateral triangle $B$ and part of the regular polygon $A$ which have a common side. The interior angle of polygon $A$ is ${165}^{\circ }$. Find the value of $y$.

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