MathDB
China TST 2004 concurrent sides

Source: China Team Selection Test 2004, Day 2, Problem 1

October 14, 2005
geometrygeometric transformationLaTeXgeometry solved

Problem Statement

Points D,E,FD,E,F are on the sides BC,CABC, CA and ABAB, respectively which satisfy EF∣∣BCEF || BC, D1D_1 is a point on BC,BC, Make D1E1∣∣DE,D1F1∣∣DFD_1E_1 || D_E, D_1F_1 || DF which intersect ACAC and ABAB at E1E_1 and F1F_1, respectively. Make △PBC∼△DEF\bigtriangleup PBC \sim \bigtriangleup DEF such that PP and AA are on the same side of BC.BC. Prove that E,E1F1,PD1E, E_1F_1, PD_1 are concurrent. [Edit by Darij: See my post #4 below for a possible correction of this problem. However, I am not sure that it is in fact the problem given at the TST... Does anyone have a reliable translation?]
Back to ProblemsView on AoPS