Problem B. 4797. (May 2016)

B. 4797. In triangle \(\displaystyle ABC\), \(\displaystyle D\), \(\displaystyle E\) and \(\displaystyle F\) are arbitrary interior points of sides \(\displaystyle AB, BC\) and \(\displaystyle CA\), respectively. Let \(\displaystyle G\), \(\displaystyle H\) and \(\displaystyle I\) denote the centroids of triangles \(\displaystyle ADF\), \(\displaystyle BED\) and \(\displaystyle CFE\), respectively. Furthermore, let \(\displaystyle S\), \(\displaystyle K\), \(\displaystyle L\) be the centroids of triangles \(\displaystyle ABC\), \(\displaystyle DEF\) and \(\displaystyle GHI\), respectively. Prove that the points \(\displaystyle K\), \(\displaystyle L\) and \(\displaystyle S\) are collinear.

Proposed by Sz. Miklós, Herceghalom

(3 pont)

Deadline expired on June 10, 2016.

Statistics:

71 students sent a solution.
3 points:	62 students.
2 points:	5 students.
1 point:	1 student.
0 point:	3 students.

Problems in Mathematics of KöMaL, May 2016