Thread: circles 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.

Originally Posted by snigdha

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.

Two simultaneous equations:

R - r = 6

πR^2 - πr^2 = 116π
EDIT: That should be R^2 + r^2 = 116.

Sorry if that error misled you.

Hello, snigdha!

Another approach . . .

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