Question 5
A5 (NET 2), IMO 5. Let $A_1A_2A_3A_4A_5A_6$ be a regular hexagon. Each of its diagonals $A_{i-1}A_{i+1}$ is divided into the same ratio $\frac\lambda{1-\lambda}$, where $0\lt \lambda\lt 1$, by a point $B_i$ in such a way that $A_i,B_i,B_{i+2}$ are collinear $(i\equiv1,\ldots,6\pmod6)$. Compute $\lambda$.