Fig.15.17, 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

Fig.15.17, shows a sector of a circle, centre O, containing an angle &#x3B8; &#xB0;. Prove that: (i) Perimeter of the shaded region is (ii) Area of the shaded region is

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.15.17, 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.15.17, 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