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Question

Figure 15.18 shows a sector of a circle of radius r cm containing an angle θ°. The area of the sector is A cm2 and perimeter of the sector is 50 cm. Prove that

(i) θ = 360θ25r-1

(ii) A = 25r − r2

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Solution

It is given that the radius of circle is r cm and angle.

(i) We know that the arc length l of a sector of an angle θ in a circle of radius r is

Now we substitute the value of OB, OA and l to find the perimeter of sector AOB,

(ii) We know that area A of the sector at an angle θ in the circle of radius r is

. Thus

Substituting the value of θ,


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