IMO Shortlist 1987 problem 10
Kvaliteta:
Avg: 0,0Težina:
Avg: 0,0 Let
and
be two spheres with distinct radii that touch externally. The spheres lie inside a cone
, and each sphere touches the cone in a full circle. Inside the cone there are
additional solid spheres arranged in a ring in such a way that each solid sphere touches the cone
, both of the spheres
and
externally, as well as the two neighboring solid spheres. What are the possible values of
?
Proposed by Iceland.
![S_1](/media/m/7/7/e/77ed808eaa71be903a10ce754f90a904.png)
![S_2](/media/m/c/1/1/c11855875777bfedb764b27ccc108413.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
![S_1](/media/m/7/7/e/77ed808eaa71be903a10ce754f90a904.png)
![S_2](/media/m/c/1/1/c11855875777bfedb764b27ccc108413.png)
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
Proposed by Iceland.
Izvor: Međunarodna matematička olimpijada, shortlist 1987