GCSE · Circles, arcs & sectors

Parts of a circleExam-style questions

The names of the parts of a circle and how to tell them apart: centre, radius, diameter and circumference; chords, arcs and tangents; sectors and segments, minor and major. Why the diameter is twice the radius, and how two radii make an isosceles triangle.

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13 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4

1
A logo is made from one large circle and three identical small circles.

The centres of all four circles lie on a straight line. The three small circles fit exactly across a diameter of the large circle. They touch each other and the large circle, as shown.Diagram NOT accurately drawn

The radius of the large circle is $18$ cm.
(a) Work out the radius of one of the small circles.

(3 marks)
(b) Work out the distance between the centres of the two outer small circles.

(2 marks)
Level 4 · 5 marksTry it
2
$A$ , $B$ and $C$ are points on a circle, centre $O$ .

Angle $AOB = 100°$

Angle $BOC = 140°$ Diagram NOT accurately drawn

Work out the size of angle $ABC$ .

Give a reason for each stage of your working.

(5 marks)
Level 4 · 5 marksTry it
3
Nia makes circular coasters from sheets of cork.

Each coaster has a radius of $4.5$ cm.

Each sheet of cork is a rectangle $50$ cm long and $30$ cm wide.

Nia cuts the coasters in rows, as shown in the diagram.Diagram NOT accurately drawn

She sells each coaster for £ $2.40$

Work out the greatest amount of money Nia can get by selling the coasters she cuts from one sheet.

You must show how you get your answer.

(5 marks)
Level 4 · 5 marksTry it