Complex with Geometry

Consider the circle $|z-5i| = 3$ , and two points $z_1 , z_2$ on it such that $|z_1|<|z_2|$ , $\text{arg}(z_1) = \text{arg}(z_2) = \frac{\pi}{3}$ . A tangent is drawn at $z_2$ to the circle, which cuts the real axis at $z_3$ . What is the magnitude of $z_3$ ?

Give your answer correct to three decimal places.