Circles, Arcs & Sectors (Edexcel IGCSE Maths): Exam Questions

$A$ and $C$ are points on a circle, centre $O$. $AB$ and $CB$are tangents to the circle. Angle $ABC$ = 52°

Work out the size of angle $x$. Give a reason for each stage of your working.

A circle has radius 8.5cm.

Work out the circumference of the circle. Give your answer correct to 3 significant figures.

$A$ and $C$ are points on a circle, centre $O$ $DA$ is the tangent to the circle at $A$ and $DC$ is the tangent to the circle at $C$

Angle $ADC$ = 48°

Work out the size of reflex angle $AOC$

$P$ is a point on a circle with centre $O$

Write down the mathematical name of the line $OP$

A wheel on a tractor has a diameter of 160 cm.

The tractor travels 1750 metres

Work out the number of complete turns made by the wheel. Show your working clearly

A and B are points on a circle, centre O.

AC and BC are tangents to the circle.

Angle ACB = 48° .

Work out the size of angle $x$.

Give a reason for each stage of your working

$x=$............°

The diagram shows a shaded shape made from three identical semicircle, $X$, $Y$ and $Z$

$ABCDE$ is a straight line.

$AC$ is the diameter of semicircle $X$and $B$ is the centre of semicircle $X$ $BD$ is the diameter of semicircle $Y$ and $C$is the centre of semicircle $Y$ $CE$ is the diameter of semicircle $Z$ and $D$ is the centre of semicircle $Z$

$AC=BD=CE=20\mathrm{cm}$

Work out the perimeter of the shaded shape. Give your answer correct to the nearest whole number.

The diagram shows a circle and a trapezium.

The height of the trapezium is $h$ cm.

The area of the circle is equal to the area of the trapezium.

Work out the value of $h$.

Give your answer correct to 1 decimal place.