Question

Circle A has a center at `(1 ,3 )` and an area of `45 pi`. Circle B has a center at `(2 ,7 )` and an area of `75 pi`. Do the circles overlap?

Answer 1

Two circles overlap

Explanation:

Area of circle A = `pi r_1^2 = 45pi`

`r_1 = sqrt((45pi)/pi) = sqrt45`

Area of circle B = `pi r_2^2 = 75pi`

`r_2 = sqrt((75pi)/pi) = sqrt75`

Distance between the two centers `d = sqrt((2-1)^2 + (7-3)^2) = sqrt17`

Since the radii of the two circles are greater than the distance between the centers of the two circles, circles overlap.