Circle A has a center at #(1 ,4 )# and an area of #28 pi#. Circle B has a center at #(7 ,9 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

1 Answer
Mar 12, 2016

circles overlap

Explanation:

First step is to calculate the distance between the centres using the#color(blue)" distance formula "#
# d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2) #

where#(x_1,y_1)" and " (x_2,y_2)" are 2 coordinate points "#

let #(x_1,y_1)=(1,4)" and " (x_2,y_2)=(7,9) #
hence #d = sqrt((7-1)^2 +(9-4)^2 )= sqrt(6^2+5^2)=sqrt61≈ 7.81#

Now require to find radii of circles,using A = #pir^2#

circle A : # pir^2 = 28pi rArr r^2= 28 rArr r = sqrt28#

circle B : #pir^2 = 36pi rArr r^2 = 36 rArrr = sqrt36 = 6 #

radius of A + radius of B = #sqrt28 + 6 ≈ 11.292 #

since the sum of the radii > distance between centres , the circles will overlap