China Mathematical Competition (Shaanxi)

Let a line with the inclination angle of $60^{\circ }$ be drawn through the focus $F$ of the parabola $y^2=8(x+2)$. If the two intersection points of the line and the parabola are $A$ and $B$, and the perpendicular bisector of the chord $AB$ intersects the $x$-axis at the point $P$, then the length of the segment $PF$ is ( ).

(A) $\frac{16}{3}$ (B) $\frac{8}{3}$ (C) $\frac{16\sqrt{3}}{3}$ (D) $8\sqrt{3}$