MathDB
IMO Shortlist 2010 - Problem G3

Source:

July 17, 2011
geometrycircumcircleInequalitypolygonIMO Shortlist

Problem Statement

Let A1A2…AnA_1A_2 \ldots A_n be a convex polygon. Point PP inside this polygon is chosen so that its projections P1,…,PnP_1, \ldots , P_n onto lines A1A2,…,AnA1A_1A_2, \ldots , A_nA_1 respectively lie on the sides of the polygon. Prove that for arbitrary points X1,…,XnX_1, \ldots , X_n on sides A1A2,…,AnA1A_1A_2, \ldots , A_nA_1 respectively, max⁡{X1X2P1P2,…,XnX1PnP1}≥1.\max \left\{ \frac{X_1X_2}{P_1P_2}, \ldots, \frac{X_nX_1}{P_nP_1} \right\} \geq 1.
Proposed by Nairi Sedrakyan, Armenia
Back to ProblemsView on AoPS