Hello, sri340!
Did you make a sketch?
You can almost "eyeball" the answer!
Two circles are drawn in a 12-inch by 14-inch rectangle.
Each circle has a diameter of 6 inches.
If the circles do not extend beyond the rectangular region,
what is the greatest possible distance between the centers of the two circles? Code:
: - 3 - : - - - -8- - - - : - 3 - :
- *-------o-------------------------* -
: | o : o | :
: |o :3 o | 3
: | P: R | :
: o - - - o - - - o - - - - * | -
: | 3 * : | :
: |o * o : | :
: | o o * : | :
12 | o * : | 6
: | * o | :
: | * o : o | :
: | o * : o| :
: | * :Q | :
: | o o - - - o -
: | : 3 | :
: | o 3: o| 3
: | o : o | :
- *-------------------------*-------* -
: - - - - - - - 14 - - - - - - - :
The circles have centers and and radius 3.
They are placed in opposite corners of the rectangle.
Center P and Q with point R form a right triangle
. . with legs: .
Therefore: .