MathDB

2

Part of 2002 Vietnam National Olympiad

Problems(2)

Vietnam NMO 2002_2

Source:

10/26/2008
An isosceles triangle ABC ABC with AB \equal{} AC is given on the plane. A variable circle (O) (O) with center O O on the line BC BC passes through A A and does not touch either of the lines AB AB and AC AC. Let M M and N N be the second points of intersection of (O) (O) with lines AB AB and AC AC, respectively. Find the locus of the orthocenter of triangle AMN AMN.
geometrygeometric transformationreflectiongeometry proposed
Again

Source: Vietnam MO 2002, Problem 5

12/16/2004
Determine for which n n positive integer the equation: a \plus{} b \plus{} c \plus{} d \equal{} n \sqrt {abcd} has positive integer solutions.
quadraticsinequalitiesnumber theory unsolvednumber theory