A bigger circle (with center A) and a smaller circle (with

[swerve]

A bigger circle (with center A) and a smaller circle (with center B) are touching each other externally. PT and PS are the tangents drawn to these circles from an external point (as shown in the figure). What is the length of ST?



1. The radii of the bigger and the smaller circles are 9 cm and 4 cm respectively
2. PB = 52/5 cm

The OA is A

Source: e-GMAT

[Ian Stewart]

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.