# 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 :

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 :

Hope this helps.