Question

# Given figure shows a sector of a circle of radius r cm containing an angle θ∘. The area of the sector is Acm2 and the perimeter of the sector is 50 cm. Prove that θ=360π(25r−1)

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Solution

## ⇒ Perimeter of the sector =50cm⇒ r is radius of a sector and θ is angle of the sector.⇒ Perimeter of the sector =θ360o×2πr+2r⇒ 50=θ360o×2πr+2r⇒ 50−2r=θ360o×2πr∴ 2(25−r)=θ360o×2×πr∴ (25−r)×360oπr=θ∴ θ=360oπ(25r−rr)∴ θ=360oπ(25r−1)Hence Proved

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