MathDB
A parabola and a regular polygon

Source: Romanian MO 2004, Final Round, 11th Grade, Problem 1

February 26, 2006
conicsparabolageometry unsolvedgeometry

Problem Statement

Let n≥3n \geq 3 be an integer and FF be the focus of the parabola y2=2pxy^2=2px. A regular polygon A1A2…AnA_1 A_2 \ldots A_n has the center in FF and none of its vertices lie on OxOx. (FA1,(FA2,…,(FAn\left( FA_1 \right., \left( FA_2 \right., \ldots, \left( FA_n \right. intersect the parabola at B1,B2,…,BnB_1,B_2,\ldots,B_n. Prove that FB1+FB2+…+FBn>np. FB_1 + FB_2 + \ldots + FB_n > np . Calin Popescu
Back to ProblemsView on AoPS