Question

Circle A has a center at `(2 ,3 )` and a radius of `3`. Circle B has a center at `(-1 ,-2 )` and a radius of `4`. Do the circles overlap? If not, what is the smallest distance between them?

Answer 1

The circles do overlap.

Explanation:

The distance between the centers is
`color(white)("XXX")sqrt(4^2+3^2) = 5`

The total lengths of the radii is `3+4 =7`
which when measured along the line segment joining the centers is greater than the length of that line segment.

Therefore the circles must overlap.