Ratio of Lengths of Arms of Pentagram

Theorem
Consider a pentagram.


 * PentagramArmLengths.png

Let $AC$ be the length of one of the lines which span the pentagram and define it.

Let $B$ be one of the points where $AC$ intersects one of the other such lines such that $AB > AC$.

Then:
 * $\dfrac {AC} {AB} = \phi$

where $\phi$ denotes the golden mean.

Proof
Follows directly from Straight Lines Subtending Two Consecutive Angles in Regular Pentagon cut in Extreme and Mean Ratio.