Circle A has a center at (5 ,12 )(5,12) and an area of 81 pi81π. Circle B has a center at (1 ,2 )(1,2) and an area of 16 pi16π. Do the circles overlap? If not, what is the shortest distance between them?

1 Answer
Dec 19, 2017

Both the circles overlap as sum of the radii is greater than the difference between the centers

Explanation:

Radius of circle A r_1 = sqrt ((81pi) / pi) = 9r1=81ππ=9

Radius of circle B r_2 = sqrt((16pi)/pi) = 4r2=16ππ=4

Distance between the centers of the two circles d = sqrt((5-1)^2 + (12-2)^2) = sqrt 116 = 10.7703d=(51)2+(122)2=116=10.7703

r_1 + r_2 = 9 + 4 = 13 is > 10.7703 (d)r1+r2=9+4=13is>10.7703(d)

Both the circles overlap as r_1+ r_2 > dr1+r2>d