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

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In a regular hexagon $ABCDEF$, points $M$ and $N$ are identified as the midpoints of sides $\overline{CD}$ and $\overline{DE}$. The intersection point $P$ is formed by lines $\overline{AM}$ and $\overline{BN}$. The goal is to calculate the ratio $\dfrac {\overline{BP}}{\overline {PN}}$. The geometric properties of the hexagon and the midpoints play a crucial role in determining this ratio. The solution involves applying principles of symmetry and proportionality inherent in regular hexagons.
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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 $\dfrac {\overline{BP}}{\overline {PN}}$
 
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Albert said:
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 $\dfrac {\overline{BP}}{\overline {PN}}$

 

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