MathDB

2

Part of 2001 Turkey MO (2nd round)

Problems(2)

Turkey NMO 2001 Problem 2

Source: Turkey NMO 2001 Problem 2

9/30/2011
(xn)−∞<n<∞(x_{n})_{-\infty<n<\infty} is a sequence of real numbers which satisfies xn+1=xn2+107x_{n+1}=\frac{x_{n}^2+10}{7} for every n∈Zn \in \mathbb{Z}. If there exist a real upperbound for this sequence, find all the values x0x_{0} can take.
algebra unsolvedalgebra
Turkey NMO 2001 Problem 5, locus of point P_G

Source: Turkey NMO 2001 Problem 5

9/30/2011
Two nonperpendicular lines throught the point AA and a point FF on one of these lines different from AA are given. Let PGP_{G} be the intersection point of tangent lines at GG and FF to the circle through the point AA, FF and GG where GG is a point on the given line different from the line FAFA. What is the locus of PGP_{G} as GG varies.
trigonometrygeometrycircumcircleperpendicular bisectorgeometric transformationgeometry proposed