# Circle A has a center at (5 ,9 ) and an area of 96 pi. Circle B has a center at (7 ,2 ) and an area of 45 pi. Do the circles overlap?

Jan 12, 2018

Since the sum of radii 16.5062 is greater than the distance
between the two centers, the two circles overlap

#### Explanation:

Distance between the two centers

$A B = D = \sqrt{{\left(7 - 5\right)}^{2} + {\left(2 - 9\right)}^{2}} = 7.28$

Radius of circle A ${r}_{a} = \sqrt{\frac{96 \pi}{\pi}} = 9.798$

Radius of circle B ${r}_{b} = \sqrt{\frac{45 \pi}{\pi}} = 6.7082$

Sum of the two radii = 9.798 + 6.7082 = 16.5062#

Since the sum of radii 16.5062 is greater than the distance
between the two centers, the two circles overlap