Area of Segment

Q.

ABC is a right-angled triangle right angled at A. A circle is inscribed in it the lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle.

Q.

In a circle of radius 20 cm, a chord subtends a right angle at the centre. Find the area of the major segment: (use $\pi$ = $\frac{22}{7}$)

1. 2635.6 ${cm}^2$
2. 1391.9 ${cm}^2$
3. 1125.2 ${cm}^2$
4. 1142.85 ${cm}^2$

Q. Find the area of the segments shaded in figure, if CB = 12 cm, AC = 5 cm, and AB is the diameter of the circle with centre 'O' (Take $\pi$ = $\frac{22}{7}$).

1. 36.39 ${cm}^2$
2. 48.32 ${cm}^2$
3. 56.54 ${cm}^2$
4. 64 ${cm}^2$

Q.

A chord of a circle of radius $12cm$ subtends an angle of $120°$ at the centre. Find the area of the corresponding segment of the circle. (Use $\pi =$$3.14$and $\surd 3=1.73$)

Q. A chord of a circle of radius $10cm$ subtends a right angle at the centre. Find the area of the corresponding (i) Minor segment, (ii) Major segment. (use $\pi =3.14$)

Q.

The radius of the circle given above is $7cm$ and the angle subtended by the arc is ${60}^{\circ }$. If the area of $△OAB$ is $21{cm}^2$, then the area of segment $APBA$ is___ .[Take the value of $\pi$ as $\frac{22}{7}$]

1. $5.8{cm}^2$

2. $4.7{cm}^2$

3. $8{cm}^2$

4. $1{cm}^2$

Q.

A circle has a radius of $19\mathrm{in}$, how do you find the radian measure of the central angle that intercepts an arc of length $9\mathrm{in}$?

Q. Question 10
Find the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is ${60}^{\circ }$

Q.

In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]

Q.

A segment is the part of a circle that lies between a _____ and a _____.

Q. Question 7
Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two . Find the area enclosed between these circles.

Q.

Find the area of the shaded region (in $c{m}^2$) as shown in figure of the two concentric circles with centre O and radius 7 $cm$ and 14 $cm$ respectively. Given $\angle$AOC = ${40}^{\circ }$.
(use $\pi$ = $\frac{22}{7}$)

1. 42.1 $c{m}^2$

2. 51.32 $c{m}^2$

3. 67.8 $c{m}^2$

4. 96.5 $c{m}^2$

Q. A circle inscribed in an equilateral triangle.If the circumference of the circle is $176cm$, find the area of the shaded region ?

Q. The area of the shaded region

1. $30.5c{m}^2$
2. $25c{m}^2$
3. $32.5c{m}^2$
4. $29c{m}^2$

Q. In the given figure, AB is a chord of length 6 cm drawn in a circle with centre 'O'. If OM is the perpendicular bisector of length $\sqrt{27}$ cm to chord AB then, find the area of segment ABY. (Use $\pi$=$\frac{22}{7}$ and $\sqrt{27}$ = 5.2 )

1. 6.2 ${cm}^2$
2. 1.5 ${cm}^2$
3. 5.8 ${cm}^2$
4. 3.25 ${cm}^2$

Q. Find the area of the minor segment of a circle of radius 14 cm , when the angle of the corresponding sector is ${60}^{\circ }$

Q. Question 6

In the figure given, the radius of the circle is 15 cm. The angle subtended by the chord AB at the centre O is ${60}^{\circ }$. Find the area of the major and minor segments.

Q. In a circle of radius 5 units CD and AB are perpendicular diameters A of chord CH cutting AB at K is 8 unit long.The diameter AB is divided into two segments whose dirnensions are :

1. 1.25, 8.75
2. 2.75, 7.25
3. 2, 8
4. 4, 6
5. none of these

Q. Find the lengths of the arcs cut off from a circle of radius $12$ $cm$ by a chord $12$ $cm$ long. Also, find the area of the minor segment.
$[Take\pi =3.14\text{and}\sqrt{3}=1.73.]$