Question

how to solve this problem​

Answer 1

Answer:

Let the radius of the circle with center of A is r

Let the radius of the circle with centre of B is R

A/c

r + R = AB = 14 cm eqn1

Area of circle = πr^2

Sum of their areas = 130π

πr^2 + πR^2 = 130π

π (r^2 + R^2) = 130π ( π cancelled )

r^2 + R^2 = 130

As,

a^2 + b^2 = ( a + b)^2 - 2ab

So,

( r+ R )^2 - 2rR = 130

putting the value

(14)^2 - 2rR = 130

196 - 2rR = 130

196 - 130 = 2rR

2rR = 66

rR = 33 eqn2

from eqn 1 and 2

r+ R = 14

R = 14 - r eqn3

putting the value of R in equation 2

r ( 14 - r) = 33

14r - r^2 = 33

r^2 - 14r + 33 = 0

r^2 - 11r - 3r + 33

r ( r - 11 ) - 3 ( r - 11 )

( r - 11 ) ( r - 3 )

r = 11 or 3

from equation 3

R = 3 or 11