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?
1 Answer
Mar 9, 2016
no overlap , 7.6
Explanation:
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
