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Discrete points in implicit loci

Given the triangle ABC. Where to put point D on side AB in order to be equally far from the other two sides?
Getting some hint by clicking "Show solution" it seems reasonable that D must be on the angle bisector at vertex C. But actually there are two such angle bisectors, and the other one intersects the side AB in an external point. Clearly that "second" point is equally distant from lines AC and BC. By right-clicking the red points the new (intuitive) syntax of the LocusEquation command can also be seen. Important notes for teachers who want to create materials with implicit curves having discrete points:
  1. The line thickness of the implicit curve should be increased to show more than a single pixel on your screen.
  2. Also the layer level should be increased to not hide the points by other objects.