# Circle A has a center at (6 ,5 ) and an area of 6 pi. Circle B has a center at (12 ,7 ) and an area of 36 pi. Do the circles overlap?

Feb 17, 2016

Circles do overlap,

#### Explanation:

Distance between $\left(6 , 5\right)$ and $\left(12 , 7\right)$ is given by

$\sqrt{{\left(12 - 6\right)}^{2} + {\left(7 - 5\right)}^{2}}$ i.e. $\sqrt{{6}^{2} + {2}^{2}}$ i.e. $\sqrt{40} = 6.3246$

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

radius of first circle is $\sqrt{6} = 2.4495$ and

radius of second circle is $\sqrt{36} = 6$

As sum of the radius of the two circles at $8.4495$ is more than distance of $6.3246$ between them, circles do overlap,