Knights of Uqbar, Part 1
The Knights of Uqbar all carry swords that are the same length. That way, if two or more knights do battle, the winner will be decided based on skill, not sword length. In this sketch, you see the swords of two knights, Albert and Bors, about to engage in combat. A third knight, Caradoc, wants to join them. To avoid giving either of his foes an advantage, Caradoc wants to make sure that he is the same distance from both of them. He doesn't want to stand so close that he could be easily skewered, but neither does he want to stand so far away that he can't reach Albert and Bors with his sword. Find a point he could stand on so that he is just within sword's reach of Albert and Bors. What Geogebra tools can you use to help you find such a point? Is there more than one such point? Join the knights' positions with line segments. What shape does this make? You may use only the following tools: New Point, Intersect Two Objects, Segment between Two Points, Line through Two Points, Circle with Center through Point, Compass.
The sword pictures are based on https://en.wikipedia.org/wiki/File:DavidI%26squire.jpg