Question

Circle A has a radius of `4` and a center of `(5 ,3 )`. Circle B has a radius of `3` and a center of `(1 ,4 )`. If circle B is translated by `<2 ,4 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

Circles A and B overlap.

Explanation:

Circle A - `Center O_A (5,3), R_A = 4`

Circle A - `Center O_A (1,4), R_A = 3`

Circle B translated by (2,4)

New center of B `O_B ((1+2),(4+4)) => ((3),(8))`

`vec(O_A O_B) = sqrt((5-3)^2 + (3-8)^2) = sqrt29 ~~ 5.39`

Sum of radii `R_A + R_B = 4 + 3 = 7`

Since `R_A + R_B > vec(O_A O_B)`, circles A and B overlap.