Question 116
Prove that a convex polygon $A_1A_2...A_n$ has three vertices $A_i, A_j, A_k$ such that
$$
[A_iA_jA_k] \gt \frac{1}{4}[A_1A_2...A_n],
$$
where $[X_1X_2...X_m]$ denotes the area of the polygon $X_1X_2...X_m$.
$$
[A_iA_jA_k] \gt \frac{1}{4}[A_1A_2...A_n],
$$
where $[X_1X_2...X_m]$ denotes the area of the polygon $X_1X_2...X_m$.