## Exam-Style Questions.## Problems adapted from questions set for previous Mathematics exams. |

## 1. | GCSE Higher |

The points B, C, D, E and F are on a circle. DAE and CAB are straight lines and AB= BE.

Calculate the value of \(x\).

## 2. | GCSE Higher |

B, C, D and E are points on the circumference of a circle, centre O.

BD is a diameter of the circle and the diagram is not drawn to scale.

(a) Find the size of angle DBE and give a reason for your answer.

(b) Find the size of angle DBC and give a reason for your answer.

## 3. | IGCSE Extended |

In the diagram above, not drawn to scale, A, B and C are points on a circle, centre O. TA is a tangent to the circle at A and OBT is a straight line. AC is a diameter and angle OTA = 28°.

Calculate

(a) angle AOT

(b) angle ACB

(c) angle ABT

## 4. | GCSE Higher |

(a) Find \(x\), the size of angle ABC if B, C and D are all points on the circle to which AB is a tangent. The diagram is not drawn to scale.

(b) Give a reason for your answer

## 5. | GCSE Higher |

The diagram, not drawn to scale, shows chords joining points on the circumference of a circle. Prove that triangle ADE is similar to triangle BCE.

## 6. | IGCSE Extended |

The diagrams are not drawn to scale

ABCDEF is a hexagon with AB parallel to ED and BC parallel to FE. GFE and GABH are straight lines. Angle CBH = 70 Calculate the values of: (a) \(p\); (b) \(q\); (c) \(t\); (d) \(x\). |
K, P, J and N are points on a circle and KN = NP. KJ is a diameter and LKM is the tangent to the circle at K. Angle LKN = 59 Find the values of: (e) \(y\); (f) \(z\). |

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