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 = nr¹and area of the minor segment ACB