Question

Circle A has a center at `(5 ,2 )` and a radius of `2`. Circle B has a center at `(1 ,-2 )` and a radius of `1`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Smallest distance between the two circles is 2.6569

Explanation:

Given
Circle A radius `r_1 = 2`
Circle B radius `r_2 = 1`
`r_1 + r_2 = 2 + 1 = 3`

Distance between the centers `d = sqrt((5-1)^2 + (2- (-2))^2) = sqrt32 = 5.6569`

`r_1 + r_2 = 3 is < d = 5.6569`

Since d > (r_1 + r_2),
both the circles do not overlap.

Smallest distance between the circles is
`d - (r_1 + r_2) = 5.6569 - 3 = 2.6569`