Perpendicular bisectors of a triangle Draw 3 points A, B, C in the P-model. Drag A, B, C around and observe whether the perpendicular lines are concurrent. Check this by constructing a P-line orthogonal to two of the lines and see whether this is orthogonal to the other two lines. For any triangle ABC in the P-model, the 3 perpendicular bisectors of the sides always belong to a pencil. In Euclidean geometry the bisectors concur 3 at a time at 4 points.
Stereographic projection Read the explanation of stereographic projection on the web.
To use the script you have to have a reference circle in the plane representing the image of the equator. All these are tasks in spherical geometry which should be done on the image of the sphere on the plane obtained by stereographic projection. Given two points A and B construct the great circle through A and B. Task 2. Given a point A and a great circle c, construct the great circle through A that is orthogonal to c. Task 3. Given a great circle c, construct the points C1 and C2 that are the poles of c. Task 4.