Question

A semicircle is drawn with AC as diameter, another semicircle is

drawn with BC as diameter and C is the centre of the big circle. A

point is marked inside figure without looking into it. What will be

the probability of getting the point inside the shaded region, if 'r' is

the radius of the small circle?​

Answer 1

Step-by-step explanation:

Let O be the centre of the circle. Then, OA=OB=OD=r

Now, OC=r−2

and CD=6

Thus, in △ODC

OC

2

+CD

2

=OD

2

(r−2)

2

+6

2

=r

2

r

2

+4−4r+36=r

2

4r=40

r=10 cm

Area of semicircle =

2

πr

2

=

2

π(10)

2

=50π

Answer 2

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