Question

Circles A and B have the following equations `(x -4 )^2+(y +3 )^2= 25` and `(x +4 )^2+(y -1 )^2= 49`. What is the greatest possible distance between a point on circle A and another point on circle B?

Answer 1

`d = 20.9443`

Explanation:

Circles `C_1` and `C_2` have respectively centers at
`p_1=(4,-3), p_2=(-1,1)` and radius `r_1=5, r_2=7`
Their distance concerning centers is given by
`d_{12} = norm (p_1-p_2) = 8.94427`.

As we can observe is verified that
`r_1 < r_2 + norm (p_1-p_2)`
`r_2 < r_1 + norm (p_1-p_2)`
`norm (p_1-p_2) < r_1 + r_2`
so the circles intersect in two points.
In this case the maximum distance between `C_1` and `C_2` is given by
`norm (p_1-p_2) +r_1+r_2 = 20.9443`