Question

Circle A has a radius of `4` and a center of `(7 ,3 )`. Circle B has a radius of `2` and a center of `(2 ,2 )`. If circle B is translated by `<1 ,3 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

circles overlap

Explanation:

`O_A ((7),(3)), R_A = 4, O_B ((2),(2)), R_B = 2`

`O_B translated by ((1),(3))`

New coordinates of `O_B -> ((2+1),(2+3)) => ((3),(5))`

`vec(O_AO_B) = sqrt((7-3)^2 + (3-5)^2) = sqrt20 ~~ 4.47`

Sum of Radii `R_A + R_B = 4 + 2 = 6`

`R_A + R_B > vec(O_AO_B)` and both the circles overlap