Answer:
x = 13
The length of ST is 78
Step-by-step explanation:
ST and SR are tangents
From the diagram
ST = 9x - 39
SR = 6x
Note that:
Two tangents drawn from the same point external to a circle are equal
That is, ST = SR
9x - 39 = 6x
9x - 6x = 39
3x = 39
x = 39/3
x = 13
ST = 9x - 39
Suubstitute x = 13
ST = 9(13) - 39
ST = 117 - 39
ST = 78