# Two circles have the following equations (x -2 )^2+(y -4 )^2= 25  and (x +8 )^2+(y +3 )^2= 49 . Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

##### 1 Answer
Sep 6, 2016

The two circle do not overlap. The greatest possible distance = 24.2066.

#### Explanation:

Circle A , centered at (2,4), radius = 5.
Circle B, centered at (-8,-3), radius =7.
Distance from center of circle A to center of circle B :
$= \sqrt{{\left(- 3 - 4\right)}^{2} + {\left(- 8 - 2\right)}^{2}}$
$= \sqrt{{\left(- 7\right)}^{2} + {\left(- 10\right)}^{2}}$
$= \sqrt{149} = 12.2066$
since 12.2066 is greater than the sum of the two radii (5+7=12), the two circle do not overlap.
The greatest possible distance bewteen a point on circle A and a point on circle B equals (radius of circle A + distance between the two centers + radius of circle B), which is :
$5 + 12.2066 + 7 = 24.2066$
Hope this helps.