# Circle A has a radius of #2 # and a center of #(6 ,5 )#. Circle B has a radius of #3 # and a center of #(2 ,4 )#. If circle B is translated by #<1 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

##### 1 Answer

Oct 10, 2017

Circle B overlaps circle A after translation.

#### Explanation:

If circle B is translated by <

Let circle B' has a radius of

The distance

Let

This satisfies the inequation:

Therefore circle A and circle B' (translated circle B) do neither circumscribe nor inscribe. They overlap.

The figure is cited from http://examist.jp/mathematics/figure-circle/two-circle/ (Japanese)