# Circle A has a center at (-4 ,2 ) and a radius of 3 . Circle B has a center at (1 ,9 ) and a radius of 2 . Do the circles overlap? If not what is the smallest distance between them?

Jun 5, 2016

no overlap , ≈ 3.6

#### Explanation:

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

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

The 2 points here are (-4 ,2) and (1 ,9)

d=sqrt((1+4)^2+(9-2)^2))=sqrt74≈8.6

radius of A + radius of B = 3 + 2 = 5

Since sum of radii < d , then no overlap

distance = d - sum of radii = 8.6 - 5 = 3.6
graph{(y^2-4y+x^2+8x+11)(y^2-18y+x^2-2x+78)=0 [-20, 20, -10, 10]}