# Circle A has a radius of 2  and a center of (1 ,7 ). Circle B has a radius of 2  and a center of (8 ,1 ). If circle B is translated by <-4 ,3 >, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Sep 3, 2016

Circle A has a radius of 2 and a center of (1,7)
Circle B has a radius of 2 and a center of (8,1)
if circle B is translated by <-4,3>, the center will be (4,4)

#### Explanation:

distance bewteen circle A (1,7) and circle B (4,4) from center to center is
$= \sqrt{{\left(4 - 1\right)}^{2} + {\left(4 - 7\right)}^{2}} = \sqrt{{3}^{2} + {3}^{2}}$
$= \sqrt{9 + 9} = \sqrt{18} = \sqrt{9 \times 2}$
$= 3 \sqrt{2} = 4.24$
As circle A and Circle B each has a radius of 2, they do not overlap each other because 4.24 is greater than 2+2 =4 (the sum of the two radii)
the minimum distance between circle A and circle B is
$= 4.24 - 2 - 2 = 0.24$