Circle A has a center at (5 ,4 ) and a radius of 4 . Circle B has a center at (6 ,-8 ) and a radius of 2 . Do the circles overlap? If not, what is the smallest distance between them?

1 Answer

The circles do not overlap.
Smallest distance=d-S=12.04159-6=6.04159 " "units

Explanation:

From the given data:
Circle A has a center at (5,4) and a radius of 4. Circle B has a center at (6,−8) and a radius of 2. Do the circles overlap? If not, what is the smallest distance between them?

Compute the sum of the radius:
Sum S=r_a+r_b=4+2=6" "units

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((5-6)^2+(4--8)^2)

d=sqrt((-1)^2+(12)^2)

d=sqrt145=12.04159

Smallest distance=d-S=12.04159-6=6.04159

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