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Cambridge IGCSE Mathematics practice

MCQ 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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MCQ

Type

cambridge_mcq

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Topic

Circle theorems I

Exam-style question

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What is the measure of the angle between a tangent and the radius at the point of contact?.

  1. A.45°
  2. B.60°
  3. C.90°
  4. D.120°

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

Paper 2Core or Extended Mathematics2 marks

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]