Tuesday, October 12, 2010

14th Eötvös Competition Problems 1907

1.  Show that the quadratic x2 + 2mx + 2n has no rational roots for odd integers m, n. 2.  Let r be the radius of a circle through three points of a parallelogram. Show that any point inside the parallelogram is a distance ≤ r from at least one of its vertices.