Marinada '22

[lang=hr] Neka je $ABC$ šiljastokutan trokut s opisanom kružnicom $k$ i ortocentrom $H$. Pretpostavimo da pravac tangentan na opisanu kružnicu trokuta $\triangle HBC$ u $H$ siječe $k$ u točkama $D$ i $E$ tako da vrijedi $|AH|=3$, $|DH|=2$, $|EH|=6$. Nađi površinu $\triangle ABC$. [/lang] [lang=en] Let $ABC$ be an acute triangle with circumcircle $k$ and orthocenter $H$. Suppose the tangent to the circumcircle of $\triangle HBC$ at $H$ intersects $k$ at points $D$ and $E$ with $HA=3$, $HX=2$, $HY=6$. Find the area of $\triangle ABC$. [/lang]