Circle A has a center at #(1 ,8 )# and an area of #15 pi#. Circle B has a center at #(5 ,3 )# and an area of #25 pi#. Do the circles overlap?

1 Answer
Mar 27, 2016

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)=(1,8)" and " (x_2,y_2)=(5,3) #

→ d =# sqrt((5-1)^2+(3-8)^2) = sqrt(16+25) = sqrt41 ≈ 6.403 #

Now , require to find the radii of the circles.Given the area , we can calculate r , using
area of circle # = pir^2 #

circle A : # pir^2 = 15pi rArr r^2 = (15pi)/pi = 15 rArr r = sqrt15 #

circle B : # pir^2 = 25pi rArr r^2 = 25 rArr r = sqrt25 = 5 #

radius of A + radius of B = # sqrt15 + 5 ≈ 8.873 #

sum of radii > distance between centres , hence they overlap.