# Circle A has a center at (3 ,2 ) and an area of 32 pi. Circle B has a center at (9 ,2 ) and an area of 24 pi. Do the circles overlap?

Jan 8, 2018

As sum of the radii is greater than the distance between the circle centers, the circles overlap .

#### Explanation:

Circle A center (3,2), area ${A}_{A} = 32 \pi$

Circle B center (9,2), area ${A}_{B} = 24 \pi$

${r}_{A} = \sqrt{\frac{32 \pi}{\pi}} = 5.6569$

${r}_{B} = \sqrt{\frac{24 \pi}{\pi}} = 4.899$

Distance between the two centers

$d = \sqrt{{\left(9 - 3\right)}^{2} + {\left(2 - 2\right)}^{2}} = 6$

As ${r}_{A} + {r}_{B} = \textcolor{red}{10.5548}$ is greater than the distance between the centers $d = \textcolor{red}{6}$, the circles overlap.