Funatic Maths

Written on
- Paper 2

Question 9

In the diagram, OO is the centre of the circle. STST is a tangent to the circle at TT. MM and PP are points on the circle such that TM=MPTM=MP. OTOT, OPOP and TPTP are drawn. Let O^1=x\hat O_1=x.
Image
Prove, with reasons, that ST^M=14xS\hat TM=\frac{\displaystyle 1}{\displaystyle 4}x. [7]\textbf{[7]}