Question 8
Let $P$ and $Q$ be the midpoints of the diagonals $BD$ and $AC$ of the quadrilateral $ABCD$. Consider the points $M \in (BC)$, $N \in (CD)$, $R \in (PQ)$ and $S \in (AC)$ such that $\frac{BM}{MC} = \frac{DN}{NC} = \frac{PR}{RQ} = \frac{AS}{SC} = k$. Prove that the centroid of the triangle $AMN$ lies on the segment $[RS]$.
Andrei Bud
Andrei Bud