# Circle A has a center at (-9 ,8 ) and a radius of 3 . Circle B has a center at (-8 ,3 ) and a radius of 1 . Do the circles overlap? If not what is the smallest distance between them?

Aug 12, 2016

no overlap , ≈ 1.099

#### Explanation:

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

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

The 2 points here are (-9 ,8) and (-8 ,3) the centres of the circles.

let $\left({x}_{1} , {y}_{1}\right) = \left(- 9 , 8\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 8 , 3\right)$

d=sqrt((-8+9)^2+(3-8)^2)=sqrt(1+25)=sqrt26≈5.099

sum of radii = radius of A + radius of B = 3 + 1 = 4

Since sum of radii < d , then no overlap

min. distance = d - sum of radii = 5.099 - 4 = 1.099
graph{(y^2-16y+x^2+18x+136)(y^2-6y+x^2+16x+72)=0 [-25.31, 25.32, -12.66, 12.65]}