Question 5
Let $ABCDEF$ be a convex hexagon, and let $A_1,B_1,C_1,D_1,E_1,F_1$ be the midpoints of $AB,BC,CD,DE,EF,FA$, respectively. Their perimeters are $p$ and $p_1$. Suppose all interior angles of $A_1B_1C_1D_1E_1F_1$ are equal. Prove
$$p\ge\frac{2\sqrt3}{3}p_1,$$
and determine exactly when equality holds.
$$p\ge\frac{2\sqrt3}{3}p_1,$$
and determine exactly when equality holds.