Calculating Ratio of $\overline{BP}$ to $\overline {PN}$ in Hexagon $ABCDEF$

[Albert1]

Regular hexagon $ABCDEF$,points $M$ and $N$ are midpoints of $\overline{CD}$
and $\overline {DE}$ respectively, point $P$ is the intersection of $\overline {AM}$ and $\overline{BN}$
Find $\dfrac {\overline{BP}}{\overline {PN}}$

 

[Albert1]

Regular hexagon $ABCDEF$,points $M$ and $N$ are midpoints of $\overline{CD}$
and $\overline {DE}$ respectively, point $P$ is the intersection of $\overline {AM}$ and $\overline{BN}$
Find $\dfrac {\overline{BP}}{\overline {PN}}$

Spoiler

solution:

View attachment 6559