Circle A has a center at (1 ,8 ) and an area of 32 pi. Circle B has a center at (2 ,3 ) and an area of 28 pi. Do the circles overlap?

Apr 14, 2016

The circles overlap.

Explanation:

Distance from the center of Circle A to center of Circle B:
$\textcolor{w h i t e}{\text{XXX}} d = \sqrt{{\left(2 - 1\right)}^{2} + {\left(3 - 8\right)}^{2}}$
$\textcolor{w h i t e}{\text{XXXX}} = \sqrt{26} \approx 5.1$

Area of Circle (in general) $= \pi {r}^{2}$

${\text{Area}}_{A} = \pi \cdot {r}_{A}^{2} = 32 \pi$
$\textcolor{w h i t e}{\text{XXX}} {r}_{A} = \sqrt{32} = 4 \sqrt{2} \approx 5.7$

Since the radius of Circle A is greater than the distance between the centers of the two circles,
the center of Circle B is inside Circle A and the circles must overlap