Knights of Uqbar, Part 3
For this task, you may use only the following Geogebra tools: New Point, Intersect Two Objects, Segment between Two Points, Line through Two Points, Circle with Center through Point, Compass. A three-headed dragon has been terrorizing the kingdom! Six knights team up and set out to find it. They find the dragon in its lair and decide to form a circle around it. To be as effective as possible, they want to make sure that they are all evenly spaced; every knight should be within sword's reach of his two neighbors, and within sword's reach of the dragon at the circle's center. Find six points on the circle for the knights to stand on so that each knight is a sword's length from the dragon and a sword's length from each neighbor. Use Geogebra tools to help. Once you've done that, connect the knights with line segments to form a polygon. What shape do you get? Rotate the swords so that they all point to the center. What shapes do you see? How do you know? Based on your work, can you come up with a method for constructing this polygon inside of a circle using a compass and ruler?
The swords are based on https://en.wikipedia.org/wiki/File:DavidI%26squire.jpg, and the picture of the dragon is from https://en.wikipedia.org/wiki/File:Ivan_Bilibin_065.jpg.