Circle A has a center at #(4 ,-1 )# and a radius of #5 #. Circle B has a center at #(-3 ,2 )# and a radius of #2 #. Do the circles overlap? If not, what is the smallest distance between them?
1 Answer
no overlap, ≈ 0.616
Explanation:
What we have to do here is
#color(blue)"compare"# the distance ( d) between the centres of the circles to the#color(blue)"sum of the radii"# • If sum of radii > d , then circles overlap
• If sum of radii < d , then no overlap
To calculate d, use the
#color(blue)"distance formula"#
#color(red)(bar(ul(|color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(a/a)|)))#
where# (x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points"# The 2 points here are (4 ,-1) and (-3 ,2)
let
# (x_1,y_1)=(4,-1)" and " (x_2,y_2)=(-3,2)#
#d=sqrt((-3-4)^2+(2+1)^2)=sqrt(49+9)=sqrt58≈7.616# Sum of radii = radius of A + radius of B = 5 + 2 = 7
Since sum of radii < d , then no overlap
smallest distance between them = d - sum of radii
#=7.616-7=0.616#
graph{(y^2+2y+x^2-8x-8)(y^2-4y+x^2+6x+9)=0 [-20, 20, -10, 10]}
