# Circle A has a center at (5 ,7 ) and an area of 56 pi. Circle B has a center at (9 ,2 ) and an area of 44 pi. Do the circles overlap?

Jun 9, 2016

We have to compare sum of the radii of the circles to the distance between their centers.

#### Explanation:

$A = \pi {r}^{2} \to r = \sqrt{\frac{A}{\pi}}$

Circle A:
${r}_{A} = \sqrt{\frac{56 \cancel{\pi}}{\cancel{\pi}}} = \sqrt{56}$

Circle B:
${r}_{B} = \sqrt{\frac{44 \cancel{\pi}}{\cancel{\pi}}} = \sqrt{44}$

Together: ${r}_{A} + {r}_{B} = \sqrt{56} + \sqrt{44} \approx 14.12$

Distance between centers:
${D}^{2} = {\left(7 - 2\right)}^{2} + {\left(5 - - 9\right)}^{2} = {5}^{2} + {14}^{2} = 221$
$\to D = \sqrt{221} \approx 14.87$

Conclusion: they do not overlap.