What is the shortest distance, in units, between the circles $(x - 9)^2 + (y - 5)^2 = 6.25$ and $(x + 6)^2 + (y + 3)^2 = 49$? Express your answer as a decimal to the nearest tenth.
So I know that the first circle's centre is at $(9,5)$ and has a radius of $2.5$ while the second one has the centre of $(-6,-3)$ and a radius of $7$.
But I don't get how to find the shortest distance between the two circles. Somebody told me the shortest distance between the circles would be a segment connecting their centres, but I don't understand why that'd be so.
Hint: Since the circles are disjoint, find the distance between the two centers and subtract the two radii.