A cyclist rides $12\text{km}$ west and then turns right and rides $7\text{km}$. In which direction is the cyclist now travelling?

Let us trace the path of the cyclist stage by stage:
1. The cyclist starts moving towards the West direction and travels $12\text{km}$.
2. While moving towards the West, taking a right turn means facing towards the North direction.
3. The cyclist then rides $7\text{km}$ in this new direction.

Therefore, the cyclist is currently travelling in the North direction.