# Circle A has a center at (12 ,9 ) and an area of 13 pi. Circle B has a center at (3 ,1 ) and an area of 28 pi. Do the circles overlap?

Jul 3, 2017

No

#### Explanation:

Circle $A$ has a centre $\left(12 , 9\right)$ and an area of $13 \pi$. Thus:

$\pi {\left({r}_{A}\right)}^{2} = 13 \pi \implies {r}_{A} = \sqrt{13} \approx 3.61$

Circle $B$ has a centre $\left(3 , 1\right)$ and an area of $28 \pi$. Thus:

$\pi {\left({r}_{B}\right)}^{2} = 28 \pi \implies {r}_{B} = \sqrt{28} \approx 5.29$

We can find the distance $A B$ using Pythagoras:

$A {B}^{2} = {\left(12 - 3\right)}^{2} + {\left(9 - 1\right)}^{2}$
$\text{ } = {9}^{2} + {8}^{2}$
$\text{ } = 81 + 64$
$\text{ } = 145 \implies A B = \sqrt{145} \approx 12.04$

And as $A B > {r}_{A} _ {r}_{B} \implies$ The circles do not overlap.