Problem

Source: Indian postal coaching 2008

Tags: geometry, circumcircle, induction, extremal principle, combinatorics unsolved, combinatorics



Let $ A_1A_2...A_n$ be a convex polygon. Show that there exists an index $ j$ such that the circum-circle of the triangle $ A_j A_{j + 1} A_{j + 2}$ covers the polygon (here indices are read modulo n).