The Nagel line is the line on which the centroid, incenter, Nagel point and Spieker center of a triangle all lie. In this Demonstration, the blue point is the centroid, the red point is the incenter, the green point is the Nagel point and the orange point is the Spieker center. You can vary the triangle using the three locators.
Inspiration and implementation of code to handle degenerate triangle cases is taken from code used by Jay Warendorff in several of his excellent Demonstrations related to triangle lines and centers. See the first Related Links.
This was a project for Advanced Topics in Mathematics II, 2016–2017, Torrey Pines High School, San Diego, CA.