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Triangle Divided (Posted on 2010-04-15) Difficulty: 2 of 5

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.

See The Solution Submitted by Bractals    
Rating: 2.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Approach. | Comment 2 of 8 |
(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
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