Parts of a Circle

A circular arc whose radius is $42 \mathrm{cm}$, makes an angle of $60°$ at the centre. If the perimeter of the sector formed is $k \mathrm{cm}$, find $k$. Use $\mathrm{\pi }=\frac{22}{7}$.

A circular arc whose radius is $14 \mathrm{cm}$, makes an angle of $30°$ at the centre. Find the perimeter of the sector formed. Use $\mathrm{\pi }=3.14$. Correct answer up to two decimal places.

The formula for the perimeter of the sector of a circle is 

Derive the formula for the perimeter of the sector of a circle.

The minute-hand of a clock is $15 \mathrm{cm}$ long. Calculate the area swept by it in $20$ minutes. If the area is $k {\mathrm{cm}}^2$ then, write the value of $k$ as final answer. [Take $\pi =3.14$]

In the given figure, $ABCD$ is a rectangle, in which side $AB=10 \mathrm{cm}$ and $BC=7 \mathrm{cm}$. From each vertex of the rectangle, four circles with radii $3.5 \mathrm{cm}$ each are drawn. If the area of the shaded portion is $k {\mathrm{cm}}^2$, find the value of $k$. (Take $\pi =\frac{22}{7}$)

In the figure below, $\mathrm{O}$ is the centre of the circle. $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are points on the circle.

$\mathrm{m}\angle \mathrm{OAB}+\mathrm{m}\angle \mathrm{OCB} =$ ___________.

In the circle shown below, $O$ is the centre of the circle. $A, B$ and $C$ are points on the circle. $\angle \mathrm{ABC}={\mathrm{y}}^{°}$.

What is the measure of the angle subtended by the major arc $ADC$ at centre $O$?

In the picture below all angles, $\angle \mathrm{CAD}, \angle \mathrm{DBE}, \angle \mathrm{ACE}, \angle \mathrm{ADB}$ and $\angle \mathrm{BEC}$ are equal, where $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and E lie on the circle.$\mathrm{O}$ is the centre of the circle.

In the figure below, points $\mathrm{A}, \mathrm{B}$ and $\mathrm{D}$ lie on the circle and $\mathrm{O}$ is the centre of the circle.

Which of the following is equal to the measure of $\angle \mathrm{ADB}$?

Ram drew $4$ triangles $△\mathrm{ABC}, △\mathrm{ABD}, △\mathrm{ABE}$ and $△\mathrm{ABF}$ as shown below.

The measure of $\angle \mathrm{ACB} = {90}^{°}, \angle \mathrm{ADB} = {95}^{°}, \angle \mathrm{AFB} = {90}^{°}$and $\angle \mathrm{AEB} = {85}^{°}$

He marked $‘\mathrm{O}’$ as the middle point of $\mathrm{AB}$. Using $‘\mathrm{O}’$ as the centre he drew a circle.

Other than points $\mathrm{A}$ and $\mathrm{B}$, which of the following points would his circle pass through?

In the given figure, O is the centre of the circle and P, Q and R are points on the circumference.

The value of x is _____ degrees.

The minute hand of a clock is $5 \mathrm{cm}$ long. The area of the sector (in two decimal places) formed by this hand in $7$ minutes is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$.

The circumference of a circle is $22 \mathrm{cm}$. The area of its one quadrant is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$. (in three decimal places).

The length of the minute hand of a clock is $10.5 \mathrm{cm}$. The area of the sector(to two decimal places) swept by the minute hand in $10$ minutes is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$ (Take $\pi =\frac{22}{7}$)

An arc of a circle with radius $21 \mathrm{cm}$ subtends an angle of $60°$at the centre. The area of the sector formed by this arc is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$.

An arc of a circle with radius $21 \mathrm{cm}$ subtends an angle of $60°$at the centre. If the length of the arc is $k \mathrm{cm}$ then find $k$.

The length of an arc is $12 \mathrm{cm}$ and radius of a circle is $7 \mathrm{cm}$ respectively. The area of the minor sector of the circle is $\mathrm{k} {\mathrm{cm}}^2$. Find the value of $\mathrm{k}$.

Radius of a circle is $10.5 \mathrm{cm}$ and angle of the sector is $45°$.  Find the area of the minor sector of the circle, rounding off to one decimal place. (Take $\pi =\frac{22}{7}$)

Radius of a circle is $7 \mathrm{cm}$ and the angle subtended at the centre by an arc is $60°$. Find the length of the arc.(Round off to one decimal place.)