Question

There are 3 semicircles touching each other internally and one circle touching 2 of them externally and the third one internally radius of the complete circle is p/q then p+q=

Answer 1

Answer:

The sum of p and q is 13.

Step-by-step explanation:

If center of largest semi-circle (r = 3) is R1 ,the larger (r = 2) is R2 & the small one (r = 1) is R3 & whole circle one's radius is R.

Then as per considering the triangle R2 R3 R & draw a line from R to R1 it will act deviance on this triangle:

r2 r3 = 3

r2 R = 2+R

r3 R = 1+R

r1 R = 3-R  

r2 r1 = 1  

r3 r1 = 2

At R1, applying cos rule:

( 2+R )2 - 12 - ( 3-R )2 / 2 x 1 x ( 3-R )   = -{(1+R)2 - 22 - (3- R) 2 / 2 * 2 *(3-R)}

Then,

R=  12 / 14=6/7

p = 6

q = 7

So by adding p and q we get 13.

Answer 2

Answer:

it is 13.

Step-by-step explanation:

p/q = 6/7

and p + q = 13.