1)
a) This is known as the Tangent-Secant Theorem....it says that :
"When a tangent and a secant are drawn from one single external point to a circle, the square of the length of tangent segment must be equal to the product of lengths of whole secant segment and the exterior portion of secant segment."
In plain English....it says that TU^2 = TR* TS
b) RT = 9 ST = 4
We can find TU thusly :
TU^2 = TR * TS
TU^2 = RT * ST
TU^2 = (9) * (4)
TU^2 = 36 take the square root of both sides
TU = 6