Circle A has a center at #(11 ,5 )# and an area of #100 pi#. Circle B has a center at #(4 ,9 )# and an area of #36 pi#. Do the circles overlap? If not, what is the shortest distance between them?

1 Answer
Mar 21, 2016

circles overlap

Explanation:

First step is to find 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)=(11,5)" and "(x_2,y_2)=(4,9)#

substitute these values into the formula to find d

# d = sqrt((4-11)^2 + (9-5)^2) = sqrt(49+16) = sqrt65 ≈ 8.06#

Now, require to find the radii of circles A and B, given that the areas are known.

Circle A : # pir^2 = 100pi rArr r^2 = (100pi)/pi = 100 rArr r = 10 #

Circle B: #pir^2 = 36pi rArr r^2 = 36 rArr r = 6 #

radius of circle A + radius of circle B = 10 + 6 = 16

since sum of radii > distance between centres → overlap