Problem

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

Tags: geometry, geometric transformation, LaTeX, geometry solved



Points D,E,F are on the sides BC,CA and AB, respectively which satisfy EF||BC, D1 is a point on BC, Make D1E1||DE,D1F1||DF which intersect AC and AB at E1 and F1, respectively. Make PBC∼△DEF such that P and A are on the same side of BC. Prove that E,E1F1,PD1 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?]