# Circle A has a center at (2 ,1 ) and an area of 16 pi. Circle B has a center at (2 ,8 ) and an area of 67 pi. Do the circles overlap?

Feb 17, 2016

Circles do overlap

#### Explanation:

Distance between $\left(2 , 1\right)$ and $\left(2 , 8\right)$ is 8-1)=7 as $x$ coordinates are common.

As radius of a circle is given by $\pi {r}^{2}$,

radius of circle A is $\sqrt{16} = 4$ and

radius of circle B is $\sqrt{67} = 8.1854$

As sum of the radius of the two circles at $12.1854$ is more than distance of $7$ between them, circles do overlap,