Question

Circle A has a center at `(1 ,3 )` and an area of `16 pi`. Circle B has a center at `(2 ,7 )` and an area of `75 pi`. Do the circles overlap?

Answer 1

overlap

Explanation:

The 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)=(1,3)" and " (x_2,y_2)=(2,7)`

`rArr d = sqrt((2-1)^2 + (7-3)^2) = sqrt(1+16) = sqrt17 ≈ 4.123`

Now require to find the radii of the circles.

Using : area of circle = `pir^2" where r is the radius "`

Circle A : `pir^2 = 16pi rArr r^2 = 16 rArr r = 4`

Circle B : `pir^2 = 75pi rArr r^2 = 75rArr r = sqrt75 ≈ 8.66`

radius of A + radius of B = 4 + 8.66 = 10.66

Since sum of radii > distance between centres → overlap