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RD Chapter 15 Areas Related to Circles Ex 15.3 Solutions

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.

Answer - 1 : -

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.

Answer - 2 : -

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.

Answer - 3 : -

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√2 cm. Find area of both the segments. (Take π = 3.14).

Answer - 4 : -

Radius of the circle (r) = 5√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)

Answer - 5 : -

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]

Answer - 6 : - 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]

Answer - 7 : -

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).

Answer - 8 : -

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

Answer - 9 : -


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

Answer - 10 : -

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

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