Answer:
ST = 32
Step-by-step explanation:
First let's call r the radius of the circle, so:
SU = UT = r
Using the formulas of secant and tangent segments in a circle, we have that:
tangent and tangent: QR^2 = QP^2
7x - 19 = 4x + 2
3x = 21
x = 7
tangent and secant:
QP^2 = QS * QT
(4x + 2)^2 = (34 - r) * (34 + r)
900 = 1156 - r^2
r^2 = 256
r = 16
ST = SU + UT = 2*r = 16*2 = 32
