Dynamic locus lines
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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:
The following drawing provides an additional (dragging) point Z that is bound to a semicircle around A. Varying Z on the semicircle allows to vary the direction of the ray h in the range mentioned above:

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.

Two questions for further puzzling:
  1. 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!

  2. 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"!

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