Eric has assembled a convex polygon $P$ from finitely many centrally symmetric (not necessarily congruent or convex) polygonal tiles. Prove that $P$ is centrally symmetric. Proposed by Josef Tkadlec - Czech Republic
Source: IGO 2024 Intermediate Level - Problem 4
Tags: geometry
Eric has assembled a convex polygon $P$ from finitely many centrally symmetric (not necessarily congruent or convex) polygonal tiles. Prove that $P$ is centrally symmetric. Proposed by Josef Tkadlec - Czech Republic