# Circle A has a center at (8 ,1 ) and an area of 100 pi. Circle B has a center at (4 ,2 ) and an area of 36 pi. Do the circles overlap? If not, what is the shortest distance between them?

Apr 8, 2016

The circles overlap

#### Explanation:

Circle A
Area given as $100 \pi$
$\rightarrow \text{radius } {r}_{A} = 10$ (since Area $= \pi {r}^{2}$)

Distance between centers of circles
$d = \sqrt{{\left(\Delta x\right)}^{2} + {\left(\Delta y\right)}^{2}}$

$\textcolor{w h i t e}{\text{X}} = \sqrt{{\left(8 - 4\right)}^{2} + {\left(1 - 2\right)}^{2}}$

$\textcolor{w h i t e}{\text{X}} = \sqrt{17}$

Since $\sqrt{17} < 10$
The center of Circle B is inside Circle A.
so the circles must overlap.