IMO Shortlist 1973 problem 2
Dodao/la:
arhiva2. travnja 2012. Given a circle
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
, find the locus of vertices
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
of parallelograms
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
with diagonals
![AC \leq BD](/media/m/1/a/7/1a7597fd0d368f566aca0870c25aef00.png)
, such that
![BD](/media/m/1/1/f/11f65a804e5c922ee28a53b1df04d138.png)
is inside
![K](/media/m/e/1/e/e1ed1943d69f4d6a840e99c7bd199930.png)
.
%V0
Given a circle $K$, find the locus of vertices $A$ of parallelograms $ABCD$ with diagonals $AC \leq BD$, such that $BD$ is inside $K$.
Izvor: Međunarodna matematička olimpijada, shortlist 1973