Task 1: Verifying Plane Axiom 2

Erik Tou
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... 1. Draw the Euclidean line OA. 2. Construct the perpendicular Euclidean line passing through OA at A, mark intersection points on the boundary. 3. Draw Euclidean lines through the intersection points, tangent to boundary.