On a globe with center $O$, there are five points $A$, $B$, $C$, $D$, $E$. Points $A$, $B$, $C$ are all on the equator with longitudes of East $0^{\circ}$, $60^{\circ}$, and $90^{\circ}$ respectively. Points $D$ and $E$ are both on the $30^{\circ}$ North latitude line with longitudes of East $0^{\circ}$ and $180^{\circ}$ respectively. Select the correct options.
(1) The length of the equator equals the sum of the lengths of the meridians at East $0^{\circ}$ and $180^{\circ}$ (2) The length of the $45^{\circ}$ North latitude line equals $\frac{1}{2}$ of the equator's length (3) The shortest path length from $A$ to $B$ along the equator equals the path length from $D$ to the North Pole along the East $0^{\circ}$ meridian (4) The path length from $D$ to $E$ along the $30^{\circ}$ North latitude line equals the sum of the path lengths from $D$ to the North Pole along the East $0^{\circ}$ meridian and from the North Pole to $E$ along the East $180^{\circ}$ meridian (5) The line passing through the North Pole and point $A$ is perpendicular to the line passing through the North Pole and point $C$