# Thread: circles touching internally/area...

1. ## 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.

2. 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.

3. 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 $R.$
The radius of the small circle is $r.$
We see that: . $R \:=\:r+6$

The area of the large circle is: . $A_1 \:=\:\pi R^2 \:=\:\pi(r+6)^2$

The area of the small circle is: . $A_2 \:=\:\pi r^2$

The sum of the areas is $116\pi$

So we have: . $\pi(r+6)^2 + \pi r^2 \:=\:116\pi$

. . Now solve for $r.$

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# two circle touch internally the sum of thier areas is 116 sq cm and distance between their center is 6 cm find radii of the circle

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