A Level Maths Question

The question is from MadAsMaths:
Two circles, C₁ and C2, are touching each other externally, and have respective radii of 9 and 4 units.
A third circle C3, of radius r, touches C1 and C₂ externally. Given further that all three circles have a common tangent, determine the value of r.
This is the diagram in the answers: I don't know if it's very clear but essentially the largest circle is the one of radius 9. And the smallest circle is the one of radius r.
Why can the smallest circle not be the one of radius 4, so the largest circle has radius r (and the mid size circle has radius 9)?
Hope that makes sense

Suppose it could and it should have similar working. I guess the question should have said something like r was the smallest radius (or similar) or a diagram given with the question.

okay, I imagine that if it was a real exam paper it would have been more specific, I think I'll try do it the way I assumed and see if I get the same answer, or it could be that doing it this way is just easier? But thanks for responding

Sometimes questions like this are cut and paste from exam papers but sometimes not the diagram. So in a real exam either there would be a diagram or the question would be more specific. If you assumed r>9, then you should set up the same equations as madas, though from a quick look at his sheet, Id have done the yellow pythagoras first as its simply at 5-12-13 triple so you have y=12-x and that cuts down on one variable immediately (just create equations in r and x and solve for r.
Its a fairly famous question related to binomial (a+b)^2 and (a-b)^2 so radii sum and difference involving pythagoras.