Circle A has a center at (-9 ,-1 ) and a radius of 3 . Circle B has a center at (-8 ,3 ) and a radius of 1 . Do the circles overlap? If not what is the smallest distance between them?

1 Answer

The circles do not overlap.
Smallest distance between them=sqrt17-4=0.1231

Explanation:

From the given data:
Circle A has a center at (−9,−1) and a radius of 3 . Circle B has a center at (−8,3) and a radius of 1
. Do the circles overlap? If not what is the smallest distance between them?

Solution: Compute the distance from center of circle A to center of circle B.

d=sqrt((x_a-x_b)^2+(y_a-y_b)^2)

d=sqrt((-9--8)^2+(-1-3)^2)

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

d=sqrt(1+16)

d=sqrt17

d=4.1231

Compute the sum of the radii :

S=r_a+r_b=3+1=4

Smallest distance between them=sqrt17-4=0.1231

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