Mathematical and Physical Journal
for High Schools
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# 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