We will state a lemma: If $N$ is a simply connected surface with Gaussian curvature $K_N$ bounded above by $-a^2, a\lt 0$ and if $\gamma$ is a curve arclength parametrized with geodesic curvature less then $\varepsilon>0$ where $\varepsilon \lt a$. Then $d(x,\gamma^*)\leq C\varepsilon$ where $\gamma^*$ is geodesic connecting endpoints of $\gamma$ and $C$ is independent of $\gamma$. Now using this important lemma we will finish the proof of main theorem.