Answer:
The first fact to keep in mind is that there are several models of the hyperbolic plane geometry. Perhaps the best known ids the Poincaré disk model, which is different from the Poincaré half plane model. Another well known model is the Beltrami-Klein model.
In the case of the Poincaré disk model, also known as conformal disk model, the lines are circular arcs contained in the unit disk, with the main characteristic that the circles must be orthogonal to the boundary of the disc, i.e. the unit circumference.
So, your assertion in completely true.
Explanation: