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.
(In reply to Approach.
by Vee-Liem Veefessional)
This was my first thought also.
I did not use this fact in my proof, but that does not mean that it could not be used in an alternate proof.
Posted by Bractals
on 2010-04-16 08:12:58