BTW, the answer is 1

Equation of line connecting (-sqrt3, 1) to origin is

y -1 = -1/sqrt-3 (x + sqrt-3)

y = -x/sqrt-3

Line perpendicular to the above line will have slope of +sqrt-3

So, y = sqrt-3 * x

This line touches origin and point (s,t), so

t = sqrt-3 * s

t^2 = 3*s^2

We also know that radius of circle = 2 (i.e. sqrt [ (sqrt-3)^2 + 1 ])

So, s^2 + t^2 = 4

s^2 + 3*s^2 = 4

s^2 = 1

s = 1