Let P be a point in the interior of an equilateral triangle.

Three line segments connect P with the vertices of the 
triangle and three line segments connect P perpendicularly
to the sides of the triangle.

These six line segments divide the triangle into six smaller
triangles that surround P.

If u, v, w, x, y, and z denote the areas of the triangles 
around P in that order, then prove that

                     u + w + y = v + x + z.

Hi Harry.

I stipulated in my original post that the sides of ABC were of unit length 1. Hence a+b=1, and b=1-a etc. Obviously I can pick any sized unit I want, given that all the sides are the same length, so there is no loss of generality.