Marinada '23

[lang = hr] Dana su dva stošca u prostoru, baze su im u istoj ravnini i stošci su s iste strane te ravnine, prvome je središte baze u $(0,0)$ i radijus joj je $6$, a drugome je središte baze u $(2,0)$ i radijus joj je $2$. Prvom stošcu je visina $12$ a drugome $4$. Kolika je vjerojatnost da nasumično odabrana kružnica radijusa $1$ koja je u ravnini paralelnoj s ravninom u kojoj su baze stožaca (pri čemu je kružnica u potpunosti unutar većeg stošca) nema presjek s zadanim stošcima? [/lang] [lang = en] Two cones are given in space, their bases are in the same plane and the cones are on the same side of that plane, the first one has its base center at $(0,0)$ and its radius is $6$, and the second one has its base center at $(2 ,0)$ and its radius is $2$. The height of the first cone is $12$ and the second one is $4$. What is the probability that a randomly chosen circle of radius $1$ that is in a plane parallel to the plane in which the bases of the cones are (where the circle is completely inside the larger cone) does not have an intersection with the given cones? [/lang]