Question 3
Let $H$ be a convex polygon. Prove that for every real number $a\in(0,1)$ there exist six distinct points $A_1,A_2,\ldots,A_6$ on its sides, listed in clockwise order, such that
1. $\overrightarrow{A_1A_2}=\overrightarrow{A_5A_4}=a\overrightarrow{A_6A_3}$;
2. the lines $A_1A_2$ and $A_5A_4$ are at equal distances from the line $A_6A_3$.
1. $\overrightarrow{A_1A_2}=\overrightarrow{A_5A_4}=a\overrightarrow{A_6A_3}$;
2. the lines $A_1A_2$ and $A_5A_4$ are at equal distances from the line $A_6A_3$.