# Two circles have the following equations #(x +5 )^2+(y +6 )^2= 9 # and #(x +2 )^2+(y -1 )^2= 1 #. 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

One circle does not contain the other. Greatest distance

#### Explanation:

Compare the distance (d) between the centres of the circles to the sum of the radii.

1) If the sum of the radii

2) If the sum of the radii

3) If

Given Circle A, centre

Circle B, centre

The first step here is to calculate d, use the distance formula :

where

here the two points are

let

Sum of radii = radius of A

Since sum of radius

no overlap => no containment

Greatest distance =