I think that the answer is unique, and I think that it is 16.
Using Guest's diagram, the triangles QPR and QSP are similar.
The angle between QP and the tangent, call it alpha, is equal to the angle QPS and also the angle QRP.
Similarly the angle between QR and the tangent is equal to the angle QSP and also the angle QPR.
So, QP/QS = QR/QP,
QS = QP.QP/QR =225/25 = 9, so SR = 16.
That fits the approximate values that Melody found by drawing.
Alan seems to chosen the particular case where angle PQR is a right angle.
Using the angles I called alpha earlier, from the triangle PQR, tan(alpha) = 15/25 = 3/5.
From the triangle PQS, tan(alpha) = QS/15, so QS = 45/5 = 9, as above.