This is an interesting question posed by my friend James Tanton on Twitter the other day[br](link to tweet: https://twitter.com/jamestanton/status/815900001838600192)[br][br]Plot a triangle in the x-y plane, then plot the locus of points Z, where Z = (x,y,D), D being the sum of the distances from any point (x,y) in the triangle to each of the three sides of the triangle.[br][br]What is the area of the triangle formed by the locus of points?

In the above applet, you can drag points A, B and C around to create different starting triangles in the x-y plane. Point D is restricted to the triangle and its interior. Point Z is the black dot plotted in the 3D section on the right side of the screen. You can drag point D around the triangle, and it will leave a trace behind in 3D of where point Z has been. In this way you can get a picture of the triangle in question.[br][br]You can also drag the 3D view around to change the perspective, and zoom in/out. To reset the trace and try a new triangle, just hit the undo button in the top right, or reload the page. Enjoy!