Marinada '23

[lang=hr] Nakon što je podragala žabu iz prethodnog zadatka, otvorilo joj se treće oko. Njen vrt je odjednom postao Euklidska ravnina koja sadrži trokut $\triangle ABC$. U središtu upisane kružnice tog trokuta nalazi se Karla, a u središtu opisane kružnice tog trokuta najslađa žaba. Karla zna da je radijus upisane kružnice $3$, a žaba joj šapće da je radijus opisane kružnice $7$. Kolika je najmanja udaljenost od Karle i žabe? [/lang] [lang=en] After she petted the frog from the previous problem, her third eye opened. Her garden suddenly became a Euclidean plane containing the triangle $\triangle ABC$. In the center of the incircle of that triangle is Karla, and in the center of the circumcircle of that triangle is the cutest frog. Karla knows that the radius of the incircle is $3$, and the frog whispered to her that the radius of the circumcircle is $7$. What is the shortest distance from Karla and the frog? [/lang]