The Poincaré disk model is one model for hyperbolic non-Euclidean geometry. We will write "circle" when we mean a circle in the sense of inversive geometry (it is either a Euclidean circle or a Euclidean line).
We call the points and lines in the Poincaré model (when it is not clear from the context) P-points and P-lines. If a P-line m is an arc of a circle m_, then m_ is called the support or the supporting circle of m.
The points on the circle h (i.e., on the circle itself, not the interior) are called ideal points. They are not true points of the model but we will see that they represent directions at infinity. They are useful in making some constructions in the model.
P-line reflection of a P-point A in a P-line m is the inversion A' of A in the supporting circle of m. It can be shown that if A is a P-point (i.e., interior to h), then so is A'. (If the support of m is a line then A' is the line reflection of A.)
The angle between P-lines is measured as the usual angle measure between Euclidean circles.
(1) For each construction in non-Euclidean geometry, interpret the statement as a construction in the P-model using "circles" and then carry out the construction. Begin by drawing the circle h whose interior is the "universe" that you will be operating in.
(2) For P-lines, you can either draw the whole support circle orthogonal to h and just ignore the part outside or else you can also construct the arc interior to h. The latter is a bit more complicated with Sketchpad, but it looks better (and prints better, since everything is inside h). In practice you may want to keep the center of the support showing in your figure as a construction aid.