Question

AB is a diameter of semicircle ACB, where C is the
mid-point of arc ACB. Find the ratio of perimeters of
the semicircle and triangle ABC.

(a) (π+2)(√2-1) : 2
(b) (√2 +1) : (√2-1)
(c) √2 : 1
(d) π+2 : 2√2
(e)√2 +2 : 1​

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