IMO Shortlist 1978 problem 7
Dodao/la:
arhiva2. travnja 2012. We consider three distinct half-lines
![Ox, Oy, Oz](/media/m/b/9/0/b902d6186adc9230d1601c8147993cb9.png)
in a plane. Prove the existence and uniqueness of three points
![A \in Ox, B \in Oy, C \in Oz](/media/m/3/9/5/395652db55fbb7029c23a4048bd18d57.png)
such that the perimeters of the triangles
![OAB,OBC,OCA](/media/m/e/0/3/e0398294b66f114ad7610601b7d8c854.png)
are all equal to a given number
%V0
We consider three distinct half-lines $Ox, Oy, Oz$ in a plane. Prove the existence and uniqueness of three points $A \in Ox, B \in Oy, C \in Oz$ such that the perimeters of the triangles $OAB,OBC,OCA$ are all equal to a given number $2p > 0.$
Izvor: Međunarodna matematička olimpijada, shortlist 1978