Question

Circle A has a center at `(8 ,4 )` and a radius of `3`. Circle B has a center at `(-1 ,-2 )` and a radius of `4`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles are separate and there is a minimum distance between them of 3.82

Explanation:

The distance between the two centres can be calculated using this
formula which is derived from Pythagoras's theorem
`sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

substituting in the values from the question
`sqrt((8--1)^2 + (4--2)^2)`

Simplifying
`sqrt(81 +36) = 10.82`

subtracting the radii of the two circles from the distance between the two centres indicates whether they over lap, touch or are separate.

distance - radius A - radius B < 0 : the circles overlap
distance - radius A - radius B = 0 : the circles touch
distance - radius A - radius B > 0 : the circles are separate

In this case
`10.82 - 3 -4 = 3.82` (greater than 0)
The circles are separate and there is a minimum distance between them of 3.82