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?

1 Answer
Feb 14, 2017

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