MathDB

3

Part of 2008 Saint Petersburg Mathematical Olympiad

Problems(2)

St Petersburgh 2008 #3

Source:

7/23/2011
Pentagon ABCDEABCDE has circle SS inscribed into it. Side BCBC is tangent to SS at point KK. If AB=BC=CDAB=BC=CD, prove that angle EKBEKB is a right angle.
geometryangle bisectorgeometry proposed
Many roots

Source: St Petersburg Olympiad 2008, Grade 11, P3

8/30/2017
There are 20082008 trinomials x2−akx+bkx^2-a_kx+b_k where aka_k and bkb_k are all different numbers from set (1,2,...,4016)(1,2,...,4016). These trinomials has not common real roots. We mark all real roots on the OxOx-axis. Prove, that distance between some two marked points is ≤1250\leq \frac{1}{250}
algebra