# Circle A has a center at (2 ,3 ) and an area of 8 pi. Circle B has a center at (11 ,7 ) and an area of 54 pi. Do the circles overlap?

Jul 28, 2018

$\text{circles overlap}$

#### Explanation:

$\text{What we have to do here is compare the distance (d)}$
$\text{between the centres to the sum of the radii}$

• " if sum of radii">d" then circles overlap"

• " if sum of radii"< d" then no overlap"

$\text{To calculate the radii use the area formula } A = \pi {r}^{2}$

${r}_{A} = \sqrt{8} = 2 \sqrt{2} \text{ and } {r}_{B} = \sqrt{54} = 3 \sqrt{6}$

$\text{to calculate d use the "color(blue)"distance formula}$

•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

$\text{let "(x_1,y_1)=(2,3)" and } \left({x}_{2} , {y}_{2}\right) = \left(11 , 7\right)$

$d = \sqrt{{\left(11 - 2\right)}^{2} + {\left(7 - 3\right)}^{2}} = \sqrt{81 + 16} = \sqrt{97} \approx 9.85$

$\text{sum of radii } = 2 \sqrt{2} + 3 \sqrt{6} \approx 10.18$

$\text{Since sum of radii">d" then circles overlap}$
graph{((x-2)^2+(y-3)^2-(2sqrt2)^2)((x-11)^2+(y-7)^2-(3sqrt6)^2)=0 [-20, 20, -10, 10]}