Circle A has a center at #(9 ,8 )# and a radius of #2 #. Circle B has a center at #(-8 ,3 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
Mar 9, 2016
no overlap , 14.72
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 coord points "# let
#(x_1,y_1)=(9,8)" and (x_2,y_2)=(-8,3) #
# d = sqrt((-8-9)^2 +(3-8)^2)=sqrt((-17)^2+(-5)^2)#
#d = sqrt314 ≈ 17.72# now radius of A = radius of B = 2+1=3
since 3 < 17.72 there is no overlap
distance between them is 17.72 - 3 = 14.72