# Circle A has a center at (2 ,2 ) and an area of 8 pi. Circle B has a center at (13 ,6 ) and an area of 49 pi. Do the circles overlap?

Nov 27, 2016

No. Please see the explanation.

#### Explanation:

Let $A r e {a}_{A} = \text{the area of circle A} = 8 \pi$
Let $A r e {a}_{B} = \text{the area of circle B} = 49 \pi$
Let ${r}_{A} =$ radius of circle A
Let ${r}_{B} =$ radius of circle B

$A r e {a}_{A} = 8 \pi = \pi {r}_{A}^{2}$

${r}_{A} = \sqrt{8}$

$A r e {a}_{B} = 49 \pi = \pi {r}_{B}^{2}$

${r}_{B} = 7$

Let $d =$ the distance between the two centers#

$d = \sqrt{{\left(13 - 2\right)}^{2} + {\left(6 - 2\right)}^{2}}$

$d = \sqrt{{11}^{2} + {4}^{2}}$

$d = \sqrt{137}$

This distance is obviously greater than the sum of the two radii but , Let's subtract ${r}_{A} \mathmr{and} {r}_{B}$, to sure:

$\sqrt{137} - 7 - \sqrt{8} \approx 1.876$

Therefore, the circles do not overlap.