Marinada '23

[lang=hr] Karla je (nestašno) u svom vrtu umjesto vrganja našla neku čudnu sortu gljiva koju je pojela. I eto ti ga na, sad joj nije dobro. Ne zna pričinjava li joj se ili ne, ali odjednom je ona u sredini valjkastog kaveza u trokutastoj sobi, tako da kavez dira svaki zid (zidovi su beskonačno produljeni u svakom smjeru), te se na presjecima zidova nalaze stupovi. Najmanje udaljenosti stupova od nasuprotnih zidova su $2$, $3$ i $5$. Na rubu kaveza našla se mala žaba koja očito jako želi biti poljubljena, a tko zna možda i Karli bude bolje. Koja je najmanja udaljenost od Karle do žabe? [/lang] [lang=en] Karla (naughtily) found some strange type of mushroom in her garden instead of porcini mushrooms, which she ate. And there you have it, now she is feeling sick. She doesn't know if she hallucinates or not, but suddenly she is in the middle of a cylinder cage in a triangular room, so that the cage touches every wall (walls are infinitely extended in every direction), and there are pillars in the corners. The smallest distances of the pillars from the opposite walls are $2$, $3$ and $5$. There is a small frog on the edge of the cage that obviously really wants to be kissed, and who knows, maybe Karla will feel better too. What is the shortest distance from Karla to the frog? [/lang]