USAMO 1979 Problem 2

$\mathrm{N}$ is the north pole. A and $\mathrm{B}$ are points on a great circle through $\mathrm{N}$ equidistant from $\mathrm{N} . \mathrm{C}$ is a point on the equator. Show that the great circle through $\mathrm{C}$ and $\mathrm{N}$ bisects the angle $\mathrm{ACB}$ in the spherical triangle $\mathrm{ABC}$ (a spherical triangle has great circle arcs as sides).