Brownian motions in $\mathbb{R}^2$ and Cauchy distribution

Question

I can't solve this problem

Let $Z_t=(X_t,Y_t)$ a brownian motion in $\mathbb{R}^2$ and it starts in (0,1). Let $T=\inf\{t\geq 0: Y_t=0\}$. Show that $X_T$ has Cauchy distribution.

Any help is welcome. Thank you in advance