In triangle $ABC$ point $M$ is on side $AB$ such that $AM:AB=3:4$ and point $P$ is on side $BC$ such that $CP:CB=3:8$. Point $N$ is symmetric to $A$ with respect to point $P$. Prove that lines $MN$ and $AC$ are parallel.
Source: Moldova EGMO TST 2021
Tags: geometry
In triangle $ABC$ point $M$ is on side $AB$ such that $AM:AB=3:4$ and point $P$ is on side $BC$ such that $CP:CB=3:8$. Point $N$ is symmetric to $A$ with respect to point $P$. Prove that lines $MN$ and $AC$ are parallel.