Question

Two circles touch internally. The sum of the of their area is 170 pi cm Square and the distance between their centres is 4 cm .Find the radii of the circle

Answer 1

Answer:

7 cm and 11 cm

Step-by-step explanation:

Let radius of circle A be a

and radius of circle B be b

Given, a - b = 4

So, a = 4+ b

and

$\pi {a}^{2} + \pi {b}^{2} = 170\pi \\={a}^{2} + {b}^{2} = 170$

Now, putting a = 4+ b value in above equation-

$( {4 + b}^{2}) + {b}^{2} = 170 \\=16 + 8b + {b}^{2} + {b}^{2} = 170 \\={2b}^{2} + 8b - 154 = 0 \\= {2b}^{2} + 22b - 14b - 154 = 0 \\= 2b(b - 11) - 14(b + 11) = 0 \\=(b + 11)((2b - 14)) = 0$

⇒b = -11 (not possible) or b =7

Thus, b =7

a = 4 + b

a = 4+7

a = 11

Thus, the radius of the two circles are 11 cm and 7 cm.