Question

two circles touches each other externally sum of their areas is 149π cm^2 & distance between their centers is 17 cm find the radii of the circle

Answer 1

Let the radius of one circle be x.

Area of 1st circle = pix^2  ------ (1)

Then the radius of another circle will be 17 - x.

Area of the second circle = pi(17 - x)^2.   ------- (2)

Now,

Given that Sum of their areas = 149pi.

pix^2 + pi(17 - x)^2 = 149pi

pix^2 + pi(289 - 34x + x^2) = 149pi

x^2 + 289 - 34x + x^2 = 149

2x^2 - 34x + 140 = 0

x^2 - 17x + 70 = 0

x^2 - 10x - 7x + 70 = 0

x(x - 10) - 7(x - 10) = 0

(x - 7) = 0, (x - 10) = 0

x = 7,10.

Therefore the radii of the two circles are 10cm and 7cm.


Hope this helps!

Answer 2

let one of the radii be x then the other will be 17-x
so 
area of circle 1 +area of cicle 2 =149 pi
pi r1^2 + pi r2^2 =pi 149
x^2 + (17-x)^2 = 149
 by doing the calculation 
x^2 + 17^2 - 2*17x + x^2    =149
 becomes
2x^2 + 289 - 34x  =  149
on dividing 2
x^2 - 17x + 70
by splitting the middle term we will get 
x=7,10
if x= 10             ,    17-x= 7
if x =7               ,    17-x=10