Question

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?

Answer 1

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.