IMO Shortlist 1986 problem 18
Dodao/la:
arhiva2. travnja 2012. Let
![AX,BY,CZ](/media/m/c/8/d/c8d35040152039ba00d06b80bad6c93b.png)
be three cevians concurrent at an interior point
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
of a triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
. Prove that if two of the quadrangles
![DY AZ,DZBX,DXCY](/media/m/9/0/4/9048c1e325d93b087242243e3681278e.png)
are circumscribable, so is the third.
%V0
Let $AX,BY,CZ$ be three cevians concurrent at an interior point $D$ of a triangle $ABC$. Prove that if two of the quadrangles $DY AZ,DZBX,DXCY$ are circumscribable, so is the third.
Izvor: Međunarodna matematička olimpijada, shortlist 1986