IMO Shortlist 1997 problem 5
Dodao/la:
arhiva2. travnja 2012. Let
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
be a regular tetrahedron and
![M,N](/media/m/4/a/e/4aea314e80c188e04d9591538475a58a.png)
distinct points in the planes
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
and
![ADC](/media/m/b/5/b/b5ba4f2dbf8650a6779ccd5923a7f007.png)
respectively. Show that the segments
![MN,BN,MD](/media/m/3/9/3/393e7f2bfe9955b33714af36dc45223a.png)
are the sides of a triangle.
%V0
Let $ABCD$ be a regular tetrahedron and $M,N$ distinct points in the planes $ABC$ and $ADC$ respectively. Show that the segments $MN,BN,MD$ are the sides of a triangle.
Izvor: Međunarodna matematička olimpijada, shortlist 1997