# Circle A has a center at (2 ,3 ) and an area of 12 pi. Circle B has a center at (8 ,2 ) and an area of 66 pi. Do the circles overlap?

Jun 30, 2016

Yes, they do.

#### Explanation:

We have to determine the radiuses of the circles.

Recall that the area of a circle is given by $a = {r}^{2} \pi$.

color(blue)("A"_"circle A" = r^2pi

color(blue)(12π = r^2pi

color(blue)(r = sqrt(12) = 2sqrt(3)

$\textcolor{red}{\text{A"_"circle B} = {r}^{2} \pi}$

color(red)(66pi = r^2pi

$\textcolor{red}{r = \sqrt{66}}$

Now, let's graph the circles on the following cartesian plane.

*The diagram above shows the length, approximately to scale, of the radiuses of both circles A and B in all directions from the center. For example, the image tells us that Circle B's radius enters circle A's radius. *

As was explained in the last paragraph, Circle A overlaps Circle B.

Hopefully this helps!