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RD Sharma Class 10 Solutions Areas related to Circles Ex 15.3

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)
RD Sharma Class 10 Chapter 15 Areas related to Circles
Areas related to Circles Class 10 RD Sharma

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
Areas related to Circles Class 10 RD Sharma
RD Sharma Class 10 Solutions Areas related to Circles
RD Sharma Class 10 Solutions Areas related to Circles

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°
RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.3
RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles

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
RD Sharma Class 10 Solutions Areas related to Circles Exercise 15.3
RD Sharma Class 10 Solutions Chapter 15 Areas related to Circles
RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles

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°
RD Sharma Solutions Class 10 Chapter 15 Areas related to Circles
RD Sharma Class 10 Pdf Chapter 15 Areas related to Circles

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
RD Sharma Solutions Class 10 Chapter 15 Areas related to Circles
Learncbse.In Class 10 Chapter 15 Areas related to Circles

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.
Learncbse.In Class 10 Chapter 15 Areas related to Circles
Class 10 RD Sharma Solutions Chapter 15 Areas related to Circles
Class 10 RD Sharma Solutions Chapter 15 Areas related to Circles

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).
RD Sharma Class 10 Pdf Free Download Full Book Chapter 15 Areas related to Circles
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
RD Sharma Class 10 Solution Chapter 15 Areas related to Circles

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
RD Sharma Class 10 Solution Chapter 15 Areas related to Circles
Solution:
RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles
RD Sharma Class 10 Pdf Ebook Chapter 15 Areas related to Circles

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
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 15 Areas related to Circles
Solution:
Let chord AB subtends angle 0 at the centre
of a circle with radius r
Now area of the circle = nr1
and area of the minor segment ACB
RD Sharma Class 10 Book Pdf Free Download Chapter 15 Areas related to Circles
Class 10 RD Sharma Chapter 15 Areas related to Circles

Exercise 15.3

RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-1
rd-sharma-class-10-solutions-areas-related-circles-ex-15-3-q2
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-3
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-4
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-4_1
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-5
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-6
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-6_1
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-6_2
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-7
RD-Sharma-class 10-maths-Solutions-chapter 15-Areas related to Circles- Exercise 15.3-Question-7_1

RD Sharma Class 10 Solutions

  • Chapter 15 Areas related to Circles Ex 15.1
  • Chapter 15 Areas related to Circles Ex 15.2
  • Chapter 15 Areas related to Circles Ex 15.3
  • Chapter 15 Areas related to Circles Ex 15.4
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