Circle A has a center at (9 ,4 ) and a radius of 3 . Circle B has a center at (-1 ,6 ) and a radius of 5 . Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Dec 7, 2017

They do not overlap - min distance is about 2.2

Explanation:

If the distance between the two centers is less than the sum of their radii, then they overlap.

We find the distance between the centers with the Pythagorean theorem:

d = sqrt((9 - (-1))^2 + (4-6)^2)

= sqrt(100 + 4)

= 10.2 (rounding)

the two circles' radii add up to 8.

...so they do NOT overlap. Minimum distance between the circles is
10.2 - 8 = 2.2 (rounding)

GOOD LUCK