Question

Circle A has a center at `(5 ,4 )` and an area of `15 pi`. Circle B has a center at `(2 ,1 )` and an area of `75 pi`. Do the circles overlap?

Answer 1

Yes, larger circle would envelop the smaller circle.

Explanation:

Area of the circle centered at (5,4) is `15 pi`, hence its radius would be #r_1 = sqrt 15 = 3.87

[using circle area formula `pi r^2`]

Likewise the area of the circle centered at (2,1) is `75pi`, hence its radius would be `5sqrt3`=8.66

The distance between the two centres would be `sqrt((5-2)^2 +(4-1)^2)= sqrt 18= 3sqrt2`= 4.24.

Since radius of the circle centered at (2,1) is 8.66 which is greater than the distance between the two centres Plus the radius of the circle centered at (5,4), the larger circle would envelop the smaller circle.