# Blue vs Red

Geometry Level 3

$$ABCDE$$ is a regular pentagon where $$O$$ is its center. It is given $$\sin 18^\circ=\dfrac{1}{4}(\sqrt{5}-1)$$. The ratio of the blue area to the red area, $$\frac{\color{blue}[\color{blue}B\color{blue}L\color{blue}U\color{blue}E\,\color{blue}]}{{\color{red}[\,\color{red}R}{\color{red}E}{\color{red}D\,\color{red}]}}$$, can be denoted as $$\dfrac{\sqrt{a}-b}{c}$$, where $$a$$, $$b$$, and $$c$$ are positive integers. Calculate $$a+b+c$$.

×