Mathematics

Problem

Let A, B, C, D, E represent vertices of a regular pentagon ABCDE. Given the position vector of these vertices be

a

a + b

\lambda a

and

\lambda b

respectively. The ratio

\frac{AD}{BC}

is equal to a.

1 - \cos \frac{3\pi}{5} : \cos \frac{3\pi}{5}

1 + 2 \cos \frac{2\pi}{5} : \cos \frac{\pi}{5}

1 + 2 \cos \frac{\pi}{5} : 2 \cos \frac{\pi}{5}

d. None of these