Question

Circle A has a center at `(2 ,2 )` and an area of `8 pi`. Circle B has a center at `(13 ,6 )` and an area of `49 pi`. Do the circles overlap?

Answer 1

No. Please see the explanation.

Explanation:

Let `Area_A = "the area of circle A" = 8pi`
Let `Area_B = "the area of circle B" = 49pi`
Let `r_A =` radius of circle A
Let `r_B =` radius of circle B

`Area_A = 8pi = pir_A^2`

`r_A = sqrt(8)`

`Area_B = 49pi = pir_B^2`

`r_B = 7`

Let `d =` the distance between the two centers#

`d = sqrt((13 - 2)^2 + (6 - 2)^2)`

`d = sqrt(11^2 + 4^2)`

`d = sqrt(137)`

This distance is obviously greater than the sum of the two radii but , Let's subtract `r_A and r_B`, to sure:

`sqrt(137) - 7 - sqrt(8) ~~ 1.876`

Therefore, the circles do not overlap.