Conjecture #7 asks about a geometric figure that can be constructed with the given lines. We recognized that a triangle would be the best shape. However, we also wanted to be able to construct a figure with sides that are equal. The answer to this would be an isoceles triangle.
In the image above, the GSP program allows us to explore at exactly what point will be able to construct an isoceles triangle. The animation allows the movement of point A to travel around the path of c1...can you conjecture when the line passing through circle c2 will provide us with an isoceles triangle?