Marinada '24

[lang=hr] Zadana je kružnica $\omega_0$ u koju su upisane tri sukladne kružnice tako da su sve četiri kružnice međusobno tangentne. U dio ravnine između tri manje kružnice upisana je nova kružnica $\omega_1$ koja izvana dodiruje svaku od tih triju kružnica. Taj postupak upisivanja kružnica se nastavlja u beskonačnost. Ako je radijus kružnice $\omega_0$ jednak $28$, koliki je radijus kružnice $\omega_{39}$? Rješenje upišite u znanstvenom zapisu s dvije decimale, sve bez razmaka (npr. 2.80*10^(-39)). [/lang] [lang=en] A circle $\omega_0$ is given, inside of which three congruent circles are inscribed, such that all four circles are mutually tangent. In the region of the plane between the three smaller circles, a new circle $\omega_1$ is inscribed, touching each of the three circles externally. This process of inscribing circles continues infinitely. If the radius of circle $\omega_0$ is $28$, what is the radius of circle $\omega_{39}$? Write your answer in scientific notation with two decimal places, with no spaces (e.g. 2.80*10^(-39)). [/lang]