Let $P$ be a point in the interior of $\vartriangle ABC$. $R_1$, $R_2$, $R_3$ are the circumradii of $\vartriangle PAB$, $\vartriangle PBC$ and $\vartriangle PCA$ respectively. Find the minimum value of $\frac{R_1+R_2+R_3}{AB+BC+CA}$ and prove that it is the minimum.