# Circle A has a center at (1 ,4 ) and an area of 28 pi. Circle B has a center at (7 ,2 ) and an area of 8 pi. Do the circles overlap? If not, what is the shortest distance between them?

Mar 10, 2016

circles overlap

#### Explanation:

Require to find the radii of circles and the distance between their centres.

Calculate distance between centres using $\textcolor{b l u e}{\text{ distance formula }}$

$d = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}}$

where $\left({x}_{1} , {y}_{1}\right) \text{ and" (x_2,y_2)" are 2 coordinate points }$

let $\left({x}_{1} , {y}_{1}\right) = \left(1 , 4\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(7 , 2\right)$

rArr d=sqrt((7-1)^2+(2-4)^2 )= sqrt(36+4)=sqrt40 ≈ 6.325
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To calculate radii , use area of circle $= \pi {r}^{2}$

circle A :  pir^2 = 28pi rArr r^2 = 28 " and " r = sqrt28 ≈ 5.292

circle B : pir^2 = 8pi rArr r^2= 8" and " r=sqrt8 ≈ 2.828