IMO 2010 Shortlist G3
Let A1A2 ...An be a convex polygon. Point P inside this polygon is chosen so that its projections P1, ..., Pn onto lines...
Category: Geometry
Problem
Let A1A2 ...An be a convex polygon. Point P inside this polygon is chosen so that its projections P1, ..., Pn onto lines A1A2, ..., AnA1 respectively lie on the sides of the polygon. Prove that for arbitrary points X1, ..., Xn on sides A1A2, ..., AnA1 respectively, max " X1X2 P1P2 ,..., XnX1 PnP1 * ©1. (Armenia)