MathDB
6 double lengths of segments given, parallelogram wanted

Source: Polish National Olympiad 2015 2nd round, p1

August 28, 2019
geometryparallelogram

Problem Statement

Points E,F,GE, F, G lie, and on the sides BC,CA,ABBC, CA, AB, respectively of a triangle ABCABC, with 2AG=GB,2BE=EC2AG=GB, 2BE=EC and 2CF=FA2CF=FA. Points PP and QQ lie on segments EGEG and FGFG, respectively such that 2EP=PG2EP = PG and 2GQ=QF2GQ=QF. Prove that the quadrilateral AGPQAGPQ is a parallelogram.
Back to ProblemsView on AoPS