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Cambridge IGCSE Mathematics

4.7Circle theorems I

Circle theorems I in Cambridge IGCSE Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
Subtopic20 practice questions1 lesson

Overview

Core heading: Circle theorems (angle in a semicircle and tangent–radius only).

Learning objectives

What the syllabus expects you to be able to do.

  1. 4.7.1Calculate unknown angles using the angle in a semicircle and the right angle between a tangent and a radius, giving reasons.
  2. 4.7.2Extended: calculate unknown angles using the angle at the centre, angles in the same segment, opposite angles of a cyclic quadrilateral and the alternate segment theorem, giving reasons.

Lessons

  • Angle properties of circles

    20 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

Circle theorems I: sample question

1 mark

ABAB is a diameter of a circle and CC is a point on the circle. Angle BAC=27∘BAC = 27^\circ. Find angle ABCABC.

Answer in °.

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