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
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)