Circle A has a center at (2 ,3 ) and a radius of 1 . Circle B has a center at (0 ,-2 ) and a radius of 4 . Do the circles overlap? If not, what is the smallest distance between them?

Mar 20, 2016

no overlap , d ≈ 0.385

Explanation:

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

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

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

let $\left({x}_{1} , {y}_{1}\right) = \left(2 , 3\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(0 , - 2\right)$

rArr d = sqrt((0-2)^2+(-2-3)^2) = sqrt(4+25) ≈ 5.385

radius of A + radius of B = 1 + 4 = 5

since : radius of A + radius of B < distance between centres
there is no overlap.

distance between circles ≈ 5.385 - 5 ≈ 0.385