# Circle A has a radius of #3 # and a center of #(3 ,9 )#. Circle B has a radius of #2 # and a center of #(1 ,4 )#. If circle B is translated by #<3 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

No overlap between Circle A and Circle B. Minimum distance = 1.083. See explanation and the diagram below.

#### 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

The first step here is to calculate the new centre of B under the traslation, which does not change the shape of the circle only its' position.

Under a translation

To calculate d, use the distance formula :

where

here the two points are

let

Sum of radii = radius of A + radius of B

Since sum of radius

Min.D minimum distance (the red line in the daigram) :