# Circle A has a center at (2 ,3 ) and an area of 8 pi. Circle B has a center at (7 ,2 ) and an area of 64 pi. Do the circles overlap?

Mar 11, 2016

Circles overlap each other.

#### Explanation:

Distance between centers of two circles at $\left(2 , 3\right)$ and 7,2) is $\sqrt{{\left(7 - 2\right)}^{2} + {\left(2 - 3\right)}^{2}} = \sqrt{25 + 1} = \sqrt{26} = 5.1$.

Radius of a circle is given by $\sqrt{\frac{A r e a}{\pi}}$, hence

area of A circle is $\sqrt{\frac{8 \pi}{\pi}} = \sqrt{8} = 2.828$ and

area of B circle is $\sqrt{\frac{64 \pi}{\pi}} = \sqrt{64} = 8$.

As the distance between two circles at $5.1$ is less than the sum of their radii $8 + 2.828 = 10.828$, circles overlap each other.