Two circles touch internally. The sum of their areas is 116π sq. cm and distance between their centres is 6cm. Find the radii of the circles.

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- February 21st 2010, 08:42 AMsnigdhacircles touching internally/area...
**Two circles touch internally. The sum of their areas is 116π sq. cm and distance between their centres is 6cm. Find the radii of the circles.** - February 21st 2010, 10:22 AMDiagonal
- February 21st 2010, 10:45 AMSoroban
Hello, snigdha!

Another approach . . .

Quote:

Two circles touch internally.

The sum of their areas is 116π cm².

The distance between their centres is 6 cm.

Find the radii of the circles.

Code:`* * *`

* *

* *

* *

* *

- * o * -

: * | * :

: * 6

R * * | * * :

: * o * -

: * * | * * r

- * * * -

The radius of the large circle is

The radius of the small circle is

We see that: .

The area of the large circle is: .

The area of the small circle is: .

The sum of the areas is

So we have: .

. . Now solve for