On the diagonals $AC$ and $CE$ of a regular hexagon $ABCDEF$ with side $1$ we mark points$ M$ and $N$ such that $AM = CN = a$. Find $a$ if the points $B, M, N$ lie on the same line.
Problem
Source: 2011 All-Ukrainain Correspondence MO of magazine ''In the World of Mathematics'', grades 5-12 p9
Tags: geometry, hexagon, collinear, equal segments, Ukraine Correspondence