## anonymous one year ago We can relate the golden ratio to the lengths of line segments as follows. If we start with a line segment AB and locate point C on the segment such that....

1. anonymous

2. anonymous

3. ganeshie8

For part $$a$$, start with the proportion $$\dfrac{AB}{AC}=\dfrac{AC}{CB}$$ |dw:1436258443492:dw| replacing $$AB$$ by $$AC+CB$$, the proportion becomes \begin{align}\dfrac{AC+CB}{AC}&=\dfrac{AC}{CB}\\~\\ 1+\dfrac{CB}{AC}&=\dfrac{AC}{CB}\\~\\ \dfrac{CB}{AC}&=\dfrac{AC-CB}{CB}\\~\\ \dfrac{ AC}{CB}&=\dfrac{CB}{AC-CB} \end{align}