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Circle A has a center at #(9 ,-2 )# and a radius of #4 #. Circle B has a center at #(-2 ,6 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

Sophia Alfred

no overlap , 7.6

The first step is to calculate the distance betwee 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 coord points "#

let#(x_1,y_1)=(9,-2)" and "(x_2,y_2) =(-2,6)#

substitute values into distance formula

#d=sqrt((-2-9)^2+(6-(-2))^2) = sqrt(121+64)=sqrt185 ≈ 13.6#

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

Since 6 < 13.6 there is no overlap

and distance between them is 13.6 - 6 = 7.6

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Answer 2

Carson Arnold

The circles A and B do not overlap. The distance between their centers is greater than the sum of their radii. The smallest distance between the circles is the difference between the distance between their centers and the sum of their radii.

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