Shortest distance between two circles 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. 
 A: Hint: Since the circles are disjoint, find the distance between the two centers and subtract the two radii.
A: Here is another way to look at the question why the shortest distance between the circles would be a segment connecting their centres.
First imagine that you just have one circle and a point P outside of it. An intermediate question ('Question 1') is: why is the shortest distance from P to the circle a segment that (when extended) passes through the center of the circle?
I can write an answer if you want but maybe you just 'see' it in this easier case.
Now returning to the two circle case. Suppose the shortest distance is a segment from a point P on the one circle to a point Q on the other. By the answer to question 1 we know that when extending PQ, the segment passes through the center of the circle Q lies on.
But if we turn our heads 180 degrees we can use the exact same reasoning to show that when extending PQ in the other direction it moves through the center of the circle P lies on.
So the segment (when extended) connects both centers and we are done.
