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Cambridge IGCSE Mathematics practice

exam practice - Determine unknown angles and provide justifications using the following circle properties: the angle in a semicircle is 90°, the angle between a tangent and a radius is 90°, the angle at the center is double that at the circumference, angles in the same segment are equal, the opposite angles of a cyclic quadrilateral add up to 180°, and the alternate segment theorem. - Circle theorems I

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Circle theorems I

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Paper 2Core or Extended Mathematics2 marks

Circle angle properties

Diagram Description

Circle with diameter and tangent

A circle has diameter AB. Point C lies on the circle forming triangle ABC. A tangent touches the circle at point B. The radius OB is drawn from the centre O to point B. Angle ABC is unknown. Determine the size of angle ABC and justify your answer using circle properties.

  1. a

    Calculate Calculate the size of angle ABC.

    Aim for approximately 2 distinct marking points.

    [2]

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  • Topic focus: Circle theorems I.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
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Paper 2 structured question: Circle theorems I

Paper 2Core or Extended Mathematics3 marks

Diagram Description

Circle with tangent and chord

In a circle, a tangent touches the circle at point T. A chord TC is drawn. The angle between the tangent and chord at point T is 40°. Find the angle in the alternate segment of the circle and explain your reasoning.

  1. a

    Determine Determine the angle in the alternate segment of the circle.

    Aim for approximately 3 distinct marking points.

    [3]