Given the two points A and B, construct the unique hyperbolic line (i.e., the Euclidean circle orthogonal to the boundary) that passes through A and B. For each step, think about which of Euclid's postulates allow you to do the construction.

The first few steps...[br]1. Draw the Euclidean line OA.[br]2. Construct the perpendicular Euclidean line passing through OA at A, mark intersection points on the boundary.[br]3. Draw Euclidean lines through the intersection points, tangent to boundary.