Indian National Mathematics Olympiad 2004 Problems

Indian National Mathematics Olympiad 2004 Problems1.  ABCD is a convex quadrilateral. K, L, M, N are the midpoints of the sides AB, BC, CD, DA. BD bisects KM at Q. QA = QB = QC = QD, and LK/LM = CD/CB. Prove that ABCD is a square. 2.  Show that a2

Indian National Mathematics Olympiad 2000 Problems

Indian National Mathematics Olympiad 2000 Problems1.  The incircle of ABC touches BC, CA, AB at K, L, M respectively. The line through A parallel to LK meets MK at P, and the line through A parallel to MK meets LK at Q. Show that the line PQ bisects AB and bisects AC. 2.