Marinada '22

[lang=hr] Ivan i njegov sinčić rado se zabavljaju rješavajući geometrijske zadatke. Danas je Ivan svom sinčiću zadao sljedeći zadatak: "U trapezu $ABCD$ s osnovicama $\overline{AB}$ i $\overline{CD}$ je $\angle ADC=\angle ACB$. Odredi udaljenost točaka $A$ i $C$ ako je duljina srednjice trapeza $13$, a duljine osnovica odnose se kao $4:9$." Ivanov sinčić je, kao i uvijek, točno riješio zadatak. Koje je rješenje dobio Ivanov sinčić? [/lang] [lang=en] Ivan and his little son enjoy solving geometric problems. Today, Ivan gave his little son the following task: "In the trapezoid $ABCD$ with bases $\overline{AB}$ and $\overline{CD}$ , you are given that $\angle ADC=\angle ACB$. Determine the distance between points $A$ and $C$ if the length of the median of the trapezoid is $13$, and the lengths of the bases are in the ratio $4:9$." Ivan's little son, as always, solved the task correctly. What solution did Ivan's little son get? [/lang]