Question

The given figure shows a rectangle ABCD HOTS with a semi-circle and a circle inscribed inside it as shown. What is the ratio of the area of the circle to that of the semi-circl​

Answer 1

Answer:

Let the centre be

′

O

′

and the point at which the semicircle intersect CD be P. Let the radius of the semi-circle be R and the circle be

′

r

′

.

OP=R and OC=R

2

OC−OT=CC

1

−TC

1

⇒R

2

−R−2r=r

2

−r

⇒R

2

−R=r

2

+r⇒r=

2

+1

(

2

−1)

R

⇒r=(

2

−1)

2

R

Ratio of areas =r

2

:R

2

=(

2

−1)

4

:1