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

1 Answer
Mar 14, 2016

no overlap , d ≈ 2.062

Explanation:

First step is to calculate the distance between the centres using the #color(blue)" distance formula " #

# d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)#

where # (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points " #

let #(x_1,y_1)=(5,-2)" and " (x_2,y_2)=(4,6)#

hence # d = sqrt((4-5)^2 + (6-(-2))^2) = sqrt65 ≈ 8.062 #

radius of A + radius of B = 2 + 4 = 6

since sum of radii < distance between centres , no overlap

and distance between A and B ≈ 8.062 - 6 ≈ 2.062