Home > Olympiad > IMC 2011 Day 2 Problem 5

IMC 2011 Day 2 Problem 5


Let F=A_0A_1...A_n be a convex polygon in the plane. Define for all 1 \leq k \leq n-1 the operation f_k which replaces F with a new polygon f_k(F)=A_0A_1..A_{k-1}A_k^\prime A_{k+1}...A_n where A_k^\prime is the symmetric of A_k with respect to the perpendicular bisector of A_{k-1}A_{k+1}. Prove that (f_1\circ f_2 \circ f_3 \circ...\circ f_{n-1})^n(F)=F.

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