Marinada '23

[lang = hr] Let $ \omega$ be a circle with center $O$ and radius $10$, and let $H$ be a point such that $OH = 6$. A point $P$ is called special if, for all triangles $ABC$ with circumcircle $\omega$ and orthocenter $H$, we have that $P$ lies on $\triangle$ABC or in the interior of $\triangle$ ABC. Find the area of the region consisting of all special points.Round your solution to $3$ decimal places. [/lang] [lang = en] Let $ \omega$ be a circle with center $O$ and radius $10$, and let $H$ be a point such that $OH = 6$. A point $P$ is called special if, for all triangles $ABC$ with circumcircle $\omega$ and orthocenter $H$, we have that $P$ lies on $\triangle$ABC or in the interior of $\triangle$ ABC. Find the area of ​​the region consisting of all special points. Round your solution to $3$ decimal places. [/lang]