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Quadrilateral Concurrency (Posted on 2008-03-06) Difficulty: 3 of 5
 
Prove that the four lines obtained by joining each vertex of a quadrilateral to the centroid of the triangle determined by the other three vertices are concurrent.

See The Solution Submitted by Bractals    
Rating: 3.0000 (1 votes)

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PROBLEM CLARIFICATION Comment 6 of 6 |

Ckeckout the following:
  www dot geocities dot com slash bractals slash quad5 dot jpg
It shows five configurations of quadrilaterals.
The solid black lines are the sides of the
quadrilateral, the thin black lines are
construction lines to find the centroids, and
the red lines are the ones that pass through
the same point.
 1) Parallelogram where the four lines merge
    into two lines
 2) Convex
 3) Reflex
 4) Concave
 5) Concave where one of the vertices of the
    quadrilateral coincides with its
    corresponding centroid
 

  Posted by Bractals on 2008-03-09 16:00:00
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