Question

two circles touch each other internally. the sum of their areas is 130 pi cm^2 and the distance between their centres is 8cm. find the radius of the two circles..... plz answer as soon as possible

Answer 1

Answer:

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:

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