IMO Shortlist 1979 problem 25
Dodao/la:
arhiva2. travnja 2012. We consider a point
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
in a plane
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
and a point
![Q \not\in p](/media/m/6/5/b/65b1e5a4eab8ad211d5dadbc046111a2.png)
. Determine all the points
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
from
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
for which
![\frac{QP+PR}{QR}](/media/m/3/7/3/373ff159071d9b77b184011854f8c23e.png)
is maximum.
%V0
We consider a point $P$ in a plane $p$ and a point $Q \not\in p$. Determine all the points $R$ from $p$ for which $$\frac{QP+PR}{QR}$$ is maximum.
Izvor: Međunarodna matematička olimpijada, shortlist 1979