English: Four generalized circles in the hyperbolic plane are tangent at a point. The ideal circle at the boundary of the hyperbolic plane is represented with a dashed stroke, and the shaded region is outside the hyperbolic plane.

A circle (blue) lies entirely in the plane; a horosphere (red) is tangent to the ideal circle, a hypercycle (purple) extends beyond the boundary of the plane, and a geodesic (green) is the hyperbolic-plane analog of a straight line.

When one point on the cycle is stereographically projected to the origin in the plane, the reciprocal of the Euclidean diameter can be used as an analog of the curvature of a Euclidean circle.