# Circle A has a center at (2 ,9 ) and an area of 16 pi. Circle B has a center at (3 ,8 ) and an area of 67 pi. Do the circles overlap?

##### 1 Answer
Feb 17, 2016

Circles do overlap

#### Explanation:

Distance between $\left(2 , 9\right)$ and $\left(3 , 8\right)$ is given by

$\sqrt{{\left(3 - 2\right)}^{2} + {\left(8 - 9\right)}^{2}}$ i.e. $\sqrt{1 + 1}$ i.e. $\sqrt{2} = 1.4142$

As radius of a circle is given by pir^2),

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

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

As sum of the radii of the two circles at $12.1854$ is more than distance of $1.4142$ between them, circles do overlap,