In the given figure, crescent is formed by two circles which touch at point A. O is the centre of the bigger circle.

Question

In the given figure, crescent is formed by two circles which touch at point A. O is the center of the bigger circle. If CB = 9 cm and DE = 5 cm, the area of the shaded portion is

(a) 625 cm² 

(b) 614.25 cm² 

(c) 643.5 cm² 

(d) 671.35 cm²

Answer 1

Answer : (c) 643.5 cm² 

Let r and R be the radii of the inner and outer circle respectively.

Then, AB – AC = CB ⇒ 2R – 2r = 9 ⇒ 2(R – r) = 9 ...(i)

Join AD and DC

△AOD ~ △DOC

⇒ R² – 10R + 25 = R² – 9R 

⇒ R = 25 ⇒ 2(25 – r) = 9 from (i) 

⇒ 2r = 41 ⇒ r = 20.5 

∴ Area of shaded portion = π(R² – r²)