MathNet 2021 — Part 03 Question 25

Find the smallest real number $\alpha$, such that for any convex polygon $P$ of area $1$, there exists a point $M$ in the plane, such that the area of the convex hull of $P \cup Q$ is at most $\alpha$, where $Q$ is the central-symmetric figure of $P$ about $M$.
(Contributed by Qu Zhenhua and Wu Yuchi)