Question

Kindly answer me this question
Two circles touch each other internally .the sum of their areas is 130 pi. And the distance between their centers is 8cm find the radio of the two circles

Answer 1

Answer:

Step-by-step explanation:

The radius of inner circle is 3.40 cm  

The radius of outer circle  is 11.40 cm .

Step-by-step explanation:

Given as :

The sum of the area of two circle touches internally = A = 130 π  cm²

Let The center of outer circle = O

The center of inner circle = O'

The distance between centers O-O' = 8 cm

Let The radius of outer circle = R

The radius of inner circle = r

sum of the area of two circle touches internally = A = 130 π  cm²

Or, A = π R² + π r²

Or, 130 π =  π R² + π r²

Or,   R² +  r² = 130             ...... .1

Now,

As distance between centers O-O' = 8 cm

So, The difference of both radius R - r = 8

Or,  R - r = 8

Or, R = 8 + r               .........2

From eq 1 and eq 2

(8 + r)² +  r² = 130

Or, 64 + 16 r + r² = 130

Or, r² + 16 r - 66 = 0

Solving this quadratic equation

r = 3.40 , - 19.40

So, The radius of inner circle = r = 3.40 cm

Put the value of r in eq 2

R = 8 + r

Or, R = 8 + 3.40

Or, R = 11.40 cm

So, The radius of outer circle = R = 11.40 cm

Hence, The radius of inner circle is 3.40 cm and  The radius of outer circle  is 11.40 cm .Answer

Answer 2

Answer:

Step-by-step explanation:

Area of circle =πr^2

130π = πr^2

130π\π= r^2

130= r^2

✓130=r

11.4= r