## RD Sharma Class 10 Solutions Areas related to Circles Ex 15.3

### RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.3

Question 1.

AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find the area of the minor segment.

Solution:

Radius of the circle (r) = 4 cm

Length of the chord AB = 4 cm

∴ In ΔOAB

OA = OB = AB (each = 4 cm)

Question 2.

A chord PQ of length 12 cm subtends an angle of 120° at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Solution:

Length of chord PQ = 12 cm

Angle at the centre (θ) = 120°

∵ Draw OD ⊥ DQ

which bisects PQ at D and also bisects ∠POQ

Question 3.

A chord of a circle of radius 14 cm makes a right angle at the centre. Find the areas of the minor and major segments of the circle.

Solution:

Radius of the circle (r) = 14 cm

Angle at the centre (θ) = 90°

Question 4.

A ehord 10 cm long is drawn in a circle whose radius is 5\(\sqrt { 2 } \)

cm. Find area of both the segments. (Take π = 3.14).

Solution:

Radius of the circle (r) = 5\(\sqrt { 2 } \) cm

And length of chord AB = 10 cm

Question 5.

A chord AB of a circle, of radius 14 cm makes an angle of 60° at the centre of the circle. Find the area of the minor segment of the circle. (Use π = 22/7)

Solution:

Radius of the circle (r) – 14 cm

Angle at the centre subtended in the fnui

AB = 60°

Question 6.

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60°. [NCERT Exemplar]

Solution:

Given that, radius of circle (r) = 14 cm

Question 7.

A chord of a circle of radius 20 cm subtends an angle of 90° at the centre. Find the area of the corresponding major segment of the circle. (Use π = 3.14) [NCERT Exemplar]

Solution:

Let AB be the chord of a circle of radius 10 cm,

with O as the centre of the circle.

Question 8.

The radius of a circle with centre O is 5 cm (see figure). Two radii OA and OB are drawn at right angles to each other. Find the areas of the segments made by the chord AB (Take π = 3.14).

Solution:

Radius of the circle (r) = 5 cm

∵ OA and OB are at right angle

∴ ∠AOB = 90°

∵ Chord AB makes two segments which are minor segment and major segment Now area of minor segment

Question 9.

AB is the diameter of a circle, centre O. C is a point on the circumference such that ∠COB = 0. The area of the minor segment cut off by AC is equal to twice the area of the sector BOC. Prove that

Solution:

Question 10.

A chord of a circle subtends an angle of 0 at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that

Solution:

Let chord AB subtends angle 0 at the centre

of a circle with radius r

Now area of the circle = nr^{1
}and area of the minor segment ACB