All angles of the convex n-gon A1A2…An are obtuse, where n≥5. For all 1≤i≤n, Oi is the circumcenter of triangle Ai−1AiAi+1 (where A0=An and An+1=A1). Prove that the closed path O1O2…On doesn't form a convex n-gon. geometrycircumcirclepolygon