Q25 of 33 Page 12

Fig., shows a sector of a circle, centre O, containing an angle θ°. Prove that:

(i)Perimeter of the shaded region is


(ii)Area of the shaded region is


Angle subtend at centre of circle = θ


Angle OAB = 90°


(At point of contract, tangent is perpendicular to radius)


OAB is right angle triangle




Perimeter of shaded region = AB+ BC+(CA arc)





Area of shaded region = (area of triangle AOB) – (area of sector)





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