Question 22
Let $ABC$ be an equilateral triangle, and $D, E, F$ be points on $BC, CA, AB$ respectively. Let $\angle BAD = \alpha$, $\angle CBE = \beta$, $\angle ACF = \gamma$. Suppose $\alpha + \beta + \gamma \ge 120^\circ$. Prove that the union $\Sigma$ of triangular regions $BAD, CBE, ACF$ covers the triangle $ABC$.