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

Aug 12, 2016

no overlap, ≈ 2.403

Explanation:

What we have to do here is compare the distance ( d) between the centres of the circles to the 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 $\textcolor{b l u e}{\text{distance formula}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{d = \sqrt{{\left({x}_{2} - {x}_{2}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where $\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2,y_2)" are 2 coordinate points}$

here the 2 points are (2 ,-1) and (-3 ,3) the centres of the circles.

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

d=sqrt((-3-2)^2+(3+1)^2)=sqrt(25+16)=sqrt41≈6.403