Marinada '23

[lang=hr] Dana je dužina $\overline {PT}$ duljine $1$. $P$ i $T$ su na kružnicama $k_1$ i $k_2$ takvim da su im središta s različitih strana $PT$. Radius $k_1$ je $\frac{\sqrt{2}}{2}$, a $k_2$ je $\frac{\sqrt{3}}{3}$. Pravac kroz $P$ sijeće $k_1$ i $k_2$ još u $A$ i $B$. Koliko je $max |AB|$? [/lang] [lang=en] The length of $\overline {PT}$ is $1$. $P$ and $T$ are on circles $k_1$ and $k_2$ such that their centers are on different sides of $PT$. The radius of $k_1$ is $\frac{\sqrt{2}}{2}$, and that of $k_2$ is $\frac{\sqrt{3}}{3}$. The line passing through $P$ intersects $k_1$ and $k_2$ at $A$ and $B$, respectively. What is the maximum value of $|AB|$? [/lang]