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

Question

Philoid · Accepted Answer

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)

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

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