Question

Circle A has a center at `(8 ,1 )` and an area of `72 pi`. Circle B has a center at `(14 ,8 )` and an area of `48 pi`. Do the circles overlap?

Answer 1

They overlap

Explanation:

First circle has center at `c_A = (8,1)` the second at `c_B = (14,8)`
their distance is `norm {c_A-c_B} = sqrt((c_A-c_B)(c_A-c_B)) = 9.21954`
Regarding areas we have `S_A=72 pi = pi r_A^2` and `S_B = 48pi = pi r_B^2` Solving for `r_A,r_B` we have
`r_A=8.48528` and `r_B = 6.9282`. Comparing with the center distance we have `norm {c_A-c_B} < r_A+r_B` so they overlap