# Circle A has a radius of #5 # and a center of #(5 ,2 )#. Circle B has a radius of #2 # and a center of #(4 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

They do not overlap, minimum distance is

#### Explanation:

First let's move the center of circle B.

Translation simply moves the circle's center, so we can just add the translation amount to the x and y values of the center.

So now we just need to figure out if A and B overlap.

B has a radius of 2, and A has a radius 5.

So, they will overlap if A's center and B's center are less than 7 away.

Distance from A's center to B's center can be calculated using distance formula.

The distance is greater than

If you do not have a calculator to calculate the square root, we know that

The minimum distance between the circles can be calculated by taking the difference of the distance and 7.

This is because a line drawn from one center to the other will be the length of both radii plus the minimum distance between the circles.