What is the center of gravity of the perimeter of a triangle (as when a piece of wire is bent into triangular form)?

(In reply to re(2): solution by Dej Mar)

I think Wolfram Mathworld has a better definition of "Medial triangle":

 The triangle formed by joining the midpoints of the sides of a triangle.

Defining it as "the triangle formed by the line segments joining the three medians of a triangle" is confusing, as the medians are lines, and they meet in one point. How would one use line segments to join these three segments?

Geometer's Sketchpad verifies that if you form a triangle by connecting the midpoints of the sides of the original triangle, and then take the incenter of this new triangle, then that is indeed the CG of the original triangle (wire frame).  Its coordinates always agree with those calculated by my first comment, and in FrankM's latest comment. 

Posted by Charlie on 2008-05-20 11:04:47