# Circle A has a center at (11 ,2 ) and an area of 100 pi. Circle B has a center at (7 ,9 ) and an area of 36 pi. Do the circles overlap? If not, what is the shortest distance between them?

Jun 11, 2017

The circles overlap.

#### Explanation:

The radius of circle $A$ is

${r}_{A} = \sqrt{100 \frac{\pi}{\pi}} = 10$

The radius of circle $B$ is

${r}_{B} = \sqrt{36 \frac{\pi}{\pi}} = 6$

The distance between the center of circle $A$ and the center of circle $B$ is

$d = \sqrt{{\left(11 - 7\right)}^{2} + {\left(2 - 9\right)}^{2}}$

$= \sqrt{{4}^{2} + {7}^{2}}$

$\sqrt{16 + 49} = \sqrt{65}$

$= 8.06$

The sum of the radii is

${r}_{A} + {R}_{B} = 10 + 6 = 16$

Therefore,

As ${r}_{A} + {r}_{B} > d$

the circles overlap

graph{((x-11)^2+(y-2)^2-100)((x-7)^2+(y-9)^2-36)=0 [-20.64, 30.66, -8, 17.66]}