logo

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

Try the question first, then check the answer and practise the same topic again.

Attempt questionCircle theorems I revisionRevise the key idea

At a glance

2

Paper

3

Marks

Topic

Circle theorems I

Exam-style question

Try this first

Paper 2Core or Extended Mathematics3 marks

Circle angle properties

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]

0 of 1 part answered

Answer every part before opening the mark scheme.

Maths method check

  • Topic focus: Circle theorems I.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

Common mistake

No common mistake is linked to this question yet.

Related flashcards

Flashcard 1 of 6

Press Space to flip, arrows to move

Related practice questions

Question 1 of 5

Choose an answer, get feedback, then move sideways through the set.

0 of 4 attempted

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]