HMMT 2003 G10

Convex quadrilateral $M A T H$ is given with $H M / M T=3 / 4$, and $\angle A T M=\angle M A T=$ $\angle A H M=60^{\circ} . N$ is the midpoint of $M A$, and $O$ is a point on $T H$ such that lines $M T, A H, N O$ are concurrent. Find the ratio $H O / O T$.