Using Statement 1, there's only one way to draw the diagram, and we know a length, so from Statement 1 alone it must be possible to find every length - there's no need to solve anything. If we wanted to actually solve, you could draw the lines AS and BT and notice that the two right triangles those lines create are similar, and Statement 1 gives us a ratio of their sizes.

Using Statement 2, we can freely change the radius of the bigger circle, and that will change the answer to the question, so Statement 2 cannot be sufficient.