Circles, arcs and sectors

The diagram depicts a sector $AOB$ of a circle, centred at $O$, with radius $9.3\text{ cm}$. The sector angle is $260^\circ$.

May/June 2015

The diagram represents a sector of a circle with radius $3r\text{ cm}$ and angle $a\degree$, together with a circle of radius $r\text{ cm}$. The area ratio of the sector to the circle with radius $r$ cm is $8:1$.

May/June 2016

In Section B, $AC$ is a diameter of the circle, centre $O$, with radius $5\text{ cm}$. $\angle ACB = 64^\circ$. A baking tray is an open cylinder with radius $15.5\text{ cm}$ and a rim. The outer edge of the rim is a circle with radius $16.5\text{ cm}$.

May/June 2016

$OAB$ forms a sector of a circle with centre $O$ and radius $10\text{ cm}$. $\angle AOB=72^\circ$.

May/June 2017

The figure presents a sector of a circle with radius $8\text{ cm}$ and central angle $70^\circ$.

May/June 2018

The diagram depicts sector $OAB$ of a circle with centre $O$ and radius $11\text{ cm}$, and the angle $\angle AOB$ is $134^\circ$.

May/June 2018

The diagram depicts two circles that share centre $O$. The smaller circle has radius $3$ cm, and the larger circle has radius $6$ cm. Minor sector $AOB$ subtends an angle of $60^\circ$. The combined area of the shaded parts is $k\pi\,\text{cm}^2$.

May/June 2019

The diagram represents the major sector of a circle with centre $O$ and radius $3\,\text{cm}$.

May/June 2022

$OMN$ is a sector of a circle with centre $O$. $ON = 20\text{ cm}$, and the area of the sector is $30\pi\text{ cm}^2$.

May/June 2023

$OAB$ forms a minor sector of a circle, with centre $O$. $OCD$ forms a major sector of another circle, with centre $O$. $OCA$ and $ODB$ are straight lines. $OC=6\text{ cm}$ and $OA=9\text{ cm}$. The minor arc $AB$ measures $5\pi\text{ cm}$.

May/June 2025

The sectors OAB and OCD are parts of circles that each have centre $O$ and an angle of $60^{\circ}$. The radius of sector OAB is $6\,\text{cm}$. The radius of sector OCD is $9\,\text{cm}$.

May/June 2025

$OAB$ forms a sector of a circle, with centre $O$ and radius $6\text{ cm}$. $\angle AOB = 25^{\circ}$.

Oct/Nov 2015

A semicircle is shown with radii $OP$ and $OQ$ drawn in. A circle with centre $C$ touches the radii at $A$ and $B$, and also meets the semicircle at $T$. The circle has radius $1.8\text{ cm}$. $\angle BCA = 120^\circ$.

Oct/Nov 2016

The circle is centred at $O$, and AC and BD are diameters. Here, $AC = 12\,\text{cm}$ and $\angle A\hat{O}B = 130^\circ$.

Oct/Nov 2018

Diagram $A$ depicts a sector of a circle, with centre $D$ and radius $\dfrac{3}{4}y$ cm. The obtuse angle $EDF = 6x^{\circ}$. Diagram $B$ depicts a sector of a circle, with centre $P$ and radius $y$ cm. The sector angle is $x^{\circ}$.

Oct/Nov 2023

A sector of a circle with angle $60\degree$ has an arc length of $4\pi$ cm. Determine the area of the sector. State your answer, in its simplest form, in terms of $\pi$.

Oct/Nov 2024

On a circle with centre $O$, A, B, C and D are points on the circumference. AOD and OCE are straight lines. DE is tangent to the circle at D. Given that $\angle ABC = 126^\circ$ and $DE = 10.5\,\text{cm}$, Calculate the radius of the circle.

Oct/Nov 2024

The circle’s diameter is 12 cm.

Oct/Nov 2025

The sketch represents a shaded region inside a large circle with centre O. The large circle has radius 10 cm. OAB is a sector of a smaller circle, also with centre O. The smaller circle has radius 7 cm and the sector angle is 130^{\circ}. Point C lies on the circumference of the large circle, and AC = BC.

Oct/Nov 2025