Marinada '23

[lang=hr] U trokutu \(\triangle ABC, AB = AC = 10\) i \(BC = 12\). Točka $D$ leži strogo između točaka $A$ i $B$ na stranici \(\overline{AB}\), a točka $E$ leži strogo između točaka $A$ i $C$ na stranici \(\overline{AC}\) tako da vrijedi \(AD = DE = EC\). Odredi duljinu dužine $AD$. Odgovor zaokruži na 3 decimale. [/lang] [lang=en] In \(\triangle ABC, AB = AC = 10\) and \(BC = 12\). Point \(D\) lies strictly between \(A\) and \(B\) on \(\overline{AB}\) and point \(E\) lies strictly between \(A\) and \(C\) on \(\overline{AC}\) so that \(AD = DE = EC\). Find \(AD\) . Round your answer to three decimal places. [/lang]