# Circle A has a center at (8 ,1 ) and an area of 64 pi. Circle B has a center at (14 ,8 ) and an area of 48 pi. Do the circles overlap?

Sep 4, 2016

Yes, the circles overlap.

#### Explanation:

Area of Circle A = $64 \pi$
Radius (Ra) = $\pi \times {\left(R a\right)}^{2} = 64 \pi \implies R a = 8$
Area of Circle B =$48 \pi$
Radius (Rb) = $\pi \times {\left(R b\right)}^{2} = 48 \pi \implies R b = \sqrt{48} = 6.928$
distance between Circle A and Circle B (center to center)
$= \sqrt{{\left(8 - 1\right)}^{2} + {\left(14 - 8\right)}^{2}}$
$= \sqrt{{7}^{2} + {6}^{2}} = \sqrt{49 + 36}$
$= \sqrt{85} = 9.22$
As the distance between the two center points of the circles is smaller than the sum of the two radii (Ra+Rb=8+6.928=14.928), the two circles do overlap.