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

Let's trace the cyclist's movement step-by-step:
1. Initially, the cyclist moves towards the West direction for $12\text{ km}$.
2. Facing West, taking a right turn means turning towards the North direction.
3. The cyclist then rides for $7\text{ km}$ in this new direction.

Since no further turns are taken, the cyclist is currently travelling in the North direction.