Circle A has a center at (3 ,2 ) and a radius of 2 . Circle B has a center at (1 ,3 ) and a radius of 4 . Do the circles overlap? If not, what is the smallest distance between them?

1 Answer
Mar 8, 2016

circles overlap

Explanation:

First step is to find the distance between the centres using thecolor(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 the coords of 2 points "

let(x_1,y_1)=(3,2)" and " (x_2,y_2)=(1,3)

d = sqrt((1-3)^2 + (3-2)^2) = sqrt(4+1) = sqrt5 ≈ 2.236

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

since 6 > 2.236 , circles will overlap