# Circle A has a center at (3 ,2 ) and an area of 16 pi. Circle B has a center at (4 ,7 ) and an area of 80 pi. Do the circles overlap?

May 12, 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"

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

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

$\text{let "(x_1,y_1)=(3,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(4 , 7\right)$

$d = \sqrt{{\left(4 - 3\right)}^{2} + {\left(7 - 2\right)}^{2}} = \sqrt{1 + 25} = \sqrt{26} \approx 5.1$

$\text{to find the radii}$

$\text{circle A } \to \pi {r}^{2} = 16 \pi \Rightarrow {r}^{2} = 16 \Rightarrow r = 4$

$\text{circle B } \to \pi {r}^{2} = 80 \pi \Rightarrow {r}^{2} = 80 \Rightarrow r = \sqrt{80} = 4 \sqrt{5}$

$\text{sum of radii } = 4 + 4 \sqrt{5} \approx 12.94$

$\text{since sum of radii"> d" then circles overlap}$
graph{((x-3)^2+(y-2)^2-16)((x-4)^2+(y-7)^2-26)=0 [-10, 10, -5, 5]}