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
Here is a question and an incorrect answer.Question: A circular plate has a diameter of $27$ cm. Work out the radius of the plate.

Answer: $27 \times 2 = 54$ , so the radius is $54$ cm.(a) Describe the error made.

(1 mark)
(b) Write down the correct radius of the plate.

(1 mark)
Level 2 · 2 marksTry it
2
Here is a circle, centre $O$ , and two straight lines, $PQ$ and $RS$ .Not drawn accurately

Use one word to describe each of these.

Choose from

arc $\qquad$ chord $\qquad$ diameter $\qquad$ radius $\qquad$ sector $\qquad$ segment $\qquad$ tangent
(a) the line $PQ$

(1 mark)
(b) the line $RS$

(1 mark)
(c) the shaded region

(1 mark)
Level 2 · 3 marksTry it
3
Match each word to its description.

One has been done for you.

Words

chord $\qquad$ arc $\qquad$ diameter $\qquad$ tangent

Descriptions
- a straight line joining two points on the circumference $\;\longleftarrow$ chord (done for you)
- a straight line from the centre to the circumference
- part of the circumference
- a chord that passes through the centre
- a straight line that touches the circle at exactly one point
Match arc, diameter and tangent to their descriptions. One description is not used.

(3 marks)
Level 2 · 3 marksTry it
4
$A$ and $B$ are points on a circle, centre $O$ .

Angle $AOB = 64°$ Diagram NOT accurately drawn
(a) Give a reason why triangle $AOB$ is isosceles.

(1 mark)
(b) Work out the size of angle $OAB$ .

(2 marks)
Level 2 · 3 marksTry it
5
Asha has a circular rug with a radius of $85$ cm.

She wants to lay the rug flat on the floor of a corridor. The corridor is $1.6$ m wide.

Will the rug fit across the width of the corridor without being folded?

Show how you decide.

(3 marks)
Level 3 · 3 marksTry it

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