# 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?

Mar 8, 2016

circles overlap

#### Explanation:

First step is to find the distance between the centres using the$\textcolor{b l u e}{\text{ distance formula }}$

d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2

where$\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are the coords of 2 points }$

let$\left({x}_{1} , {y}_{1}\right) = \left(3 , 2\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 3\right)$

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