UNESCO Competition 1995-96

  geometry problems from  UNESCO Competition with aops links in the names

It lasted only 2 years

problem set from 1996-97 is missing

1995-96

1st UNESCO Competition 1995-6 p3

A rectangle $MNPQ$  circumscribes a triangle $ABC$ if on each of the edges $MN,NP,PQ,QM$ there is at least one vertex of $ABC$. Find the locus of the centers $O$ of rectangles $MNPQ$ which circumscribe a given triangle $ABC$.

1st UNESCO Competition 1995-6 p6

Given a segment $AB$ and a constant $k>0$. Find the locus of points $C$ in the plane such that in triangle $ABC$, the length of a side is $k$ times the length of the corresponding altitude.