#### Question

In the given figure, O is the centre of the sector. \[\angle\]ROQ = \[\angle\]MON = 60^{°} . OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN. ( \[\pi = \frac{22}{7}\])

#### Solution

In the given figure, ∠ROQ = ∠MON = θ = 60º

Radius of the sector ORXQ = OR = 7 cm

∴ Length of the arc RXQ = \[\frac{\theta}{360º} \times 2\pi r = \frac{60º }{360º } \times 2 \times \frac{22}{7} \times 7\] = 7.3 cm

Radius of the sector OMYN = OM = 21 cm

∴ Length of the arc MYN = \[\frac{\theta}{360º } \times 2\pi r = \frac{60º }{360º } \times 2 \times \frac{22}{7} \times 7\] = 22 cm

Thus, the lengths of the arc RXQ and arc MYN are 7.3 cm and 22 cm, respectively.

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Solution In the Given Figure, O is the Centre of the Sector. ∠ Roq = ∠ Mon = 60° . Or = 7 Cm, and Om = 21 Cm. Find the Lengths of Arc Rxq and Arc Myn. ( π = 22 7 ) Concept: Perimeter and Area of a Circle.