MathDB

2

Part of 2006 Iran MO (2nd round)

Problems(2)

Find all polynomials - Iran NMO 2006 - Problem2

Source:

9/23/2010
Determine all polynomials P(x,y)P(x,y) with real coefficients such that P(x+y,x−y)=2P(x,y)∀x,y∈R.P(x+y,x-y)=2P(x,y) \qquad \forall x,y\in\mathbb{R}.
algebrapolynomialalgebra proposed
Points M such that AM/BM=CM/DM - Iran NMO 2006 - Problem5

Source:

9/23/2010
Let ABCDABCD be a convex cyclic quadrilateral. Prove that: a)a) the number of points on the circumcircle of ABCDABCD, like MM, such that MAMB=MDMC\frac{MA}{MB}=\frac{MD}{MC} is 44. b)b) The diagonals of the quadrilateral which is made with these points are perpendicular to each other.
geometrycircumcircleangle bisectorgeometry proposed