In a triangle $ABC$ the altitude $AD$ is drawn. Points $M$ on side $AC$ and $N$ on side $AB$ are taken so that $\angle MDA=\angle NDA$. Prove that the lines $AD,BM$ and $CN$ are concurrent.
Source: 2001 Moldova MO Grade 9 P4
Tags: geometry
In a triangle $ABC$ the altitude $AD$ is drawn. Points $M$ on side $AC$ and $N$ on side $AB$ are taken so that $\angle MDA=\angle NDA$. Prove that the lines $AD,BM$ and $CN$ are concurrent.