An angle is given and two points $M$ and $N$ inside it. Through these two points, draw parallel lines $m$ and $n$ so that lengths formed by their intersections with the angle arms are in ratio 1:3.
I tried solving it with homothety but it didn't quite work out. I would appreciate any hints.
One solution :
Hint: Let the vertex of the angle be $A$. Mark point $P$ on $\overrightarrow{AM}$ such that $|MP|=2|AM|$. Then $\overleftrightarrow{NP}$ must be the line $n$. Can you find line $m$ ? Why does the construction work and is it unique ?