Here, we introduce the Poincare disc model of hyperbolic geometry. Our description uses ideas from inversive geometry.

We can get a similar model for euclidean geometry. 
The set is the open disc D:{z : z < 1} in the complex plane. Note. The boundary of D is the unit circle C: {z : z = 1}. The points of C do not belong to the geometry, but they play a role similar to the points at infinity in euclidean geometry.
Definition A hyperbolic line (or
hline) is a subset of D
An iline L is either an extended line or a circle. Observe that The concept of orthogonal circles is less familiar. We have the following facts:
The figure illustrates the hline obtained from the point P.

