Q. 54.2( 309 Votes )

# In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find:

(i) The length of the arc

(ii) Area of the sector formed by the arc

(iii) Area of the segment formed by the corresponding chord.

Answer :

Radius (*r*) of circle = 21 cm

The angle subtended by the given arc = 60°

Length of an arc of a sector of angle θ =

(i) Length of arc ACB =

= × 2 × 22 × 3

= 22 cm

(ii) Area of sector OACB =

=

= × × 21 × 21

= 231 cm^{2}

**(iii)** In ΔOAB,

⇒ ∠OAB = ∠OBA (Angles opposite to equal sides are equal)

⇒ ∠OAB + ∠AOB + ∠OBA = 180°

⇒ 2∠OAB + 60° = 180°

⇒ 2∠OAB = 180° - 60°⇒ ∠OAB = 60°

Hence,

ΔOAB is an equilateral triangle

Area of equilateral triangle = (Side)^{2}

⇒ Area of ΔOAB = (Side)^{2}

= × (21)^{2}

= cm^{2}

Area of segment ACB = Area of sector OACB - Area of ΔOAB

= (231 - ) cm^{2}

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PREVIOUSA chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding:
(i) Minor segment
(ii) Major sector (Use π = 3.14)NEXTA chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle(Use π = 3.14 and = 1.73)

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