Where do all the points lie from which a given segment appears under a right angle? The following construction will help to answer this (classical) question:

- A segment [AB] is given. Now construct a ray h that starts in the point A. The angle between the segment and the ray may vary in the range [-90°.....+90°].
- Raise the perpendicular g from point B on the line h, and mark its foot as C.

When you now record the positions of C, while Z runs through the whole semicircle, you get the locus line of the point C. Obviously, this locus line is the (full) Thales circle over [AB]:

When you drag A or B, not only g, h and C are redrawn, but also the locus line itself is recalculated and updated.

- Why is Z bound to a semicircle and not to a full circle? How does the locus line change when you use a full circle? Construct an appropriate drawing and try it!
- Is it possible to bind Z to a straight line, too? Construct a drawing and try to find the best possible position for this "carrier line"!