Four circles $\omega_1, \omega_2, \omega_3, \omega_4$ intersects at a single point $P$. The pairs $\omega_1$ and $\omega_2$, $\omega_2$ and $\omega_3$, $\omega_3$ and $\omega_4$, $\omega_4$ and $\omega_1$ intersects at points $A, B, C, D$ respectively. If$AB = 6, BC = 4, CD = 3, PD = 5, AD = 2$, find the distance between point $P$ and $B$.