a fundamental arc on a cycle is an arc such that the tangent

a fundamental arc on a cycle is an arc such that the tangent at one end is parallel to the diameter at the other end. Draw examples of fundamental arc on (a) a circle in Euclidean geometry, (b) a hyperbolic circle, and (c) a horocycle.

Solution

In (b) and (c), you may assume that the point of tangency is the origin in the unit disk model of hyperbolic geometry, and in (c), you may assume that the ideal point of the horocycle is Â.