# Circle A has a center at (2 ,3 ) and an area of 12 pi. Circle B has a center at (7 ,2 ) and an area of 64 pi. Do the circles overlap?

##### 1 Answer
Dec 20, 2017

Both the circles overlap

#### Explanation:

Circle A radius ${r}_{1} = \sqrt{\frac{12 \pi}{\pi}} = 2 \sqrt{3} = 3.4641$

Circle B radius ${r}_{2} = \sqrt{\frac{64 \pi}{\pi}} = 8$

Distance between the centers $d = \sqrt{{\left(7 - 2\right)}^{2} + {\left(2 - 3\right)}^{2}} = 5.099$

Sum of the radii ${r}_{1}$ & ${r}_{2}$ ( 11.4641 ) is greater than the distance between the centers d (5.099); hence the circles overlap.