In triangle $ABC$ holds $\angle ACB = 90^{\circ}$, $\angle BAC = 30^{\circ}$ and $BC=1$. In triangle $ABC$ is inscribed equilateral triangle (every side of a triangle $ABC$ contains one vertex of inscribed triangle). Find the least possible value of side of inscribed equilateral triangle
Problem
Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009
Tags: geometry, inscribed triangle