5

Part of 2024 China Western Mathematical Olympiad

Problems(1)

Hexagon in a square

Source: 2024 CWMO P5

\mathcal{P}

inscribed in a unit square, such that each vertex is on the side of the square. It’s known that all interior angles of the hexagon are equal. Find the maximum possible value of the smallest side length of

\mathcal{P}