Question

Circle A has a radius of `3` and a center of `(5 ,9 )`. Circle B has a radius of `4` and a center of `(1 ,2 )`. If circle B is translated by `<3 ,2 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

`R_A + R_B` `color(green)((7))` `>` `vec(O_AO_B)` `color(blue)((4.123))`, the two circles A & B overlap.

Explanation:

Circle A `O_A (5,9), R_A = 3`, Circle B `O_B (1,2), R_B = 4`

`O_B` `translated` `by` `(3,2)`

New `O_B = ((1+3),(2+3)) => ((4),(5))`

Distance `vec(O_AO_B) = sqrt((4-5)^2 + (5-9)^2) = sqrt17 ~~ 4.123`

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

Since `R_A + R_B` `color(green)((7))` `>` `vec(O_AO_B)` `color(blue)((4.123))`, the two circles A & B overlap.