I can't to color all area of the inscribed angle. When I color, appears only the triangle (not a curvilineo triangle)
\begin{center}
\begin{tikzpicture}[scale=0.7]
\draw[fill=gray!40] (0,0) --(2.5,4.3)--(7.5,4.3)--(0,0);
\draw[ultra thick]
(0,0)--(10,0)
(0,0)--(2.5,4.3)
(0,0)--(7.5,4.3);
\draw[ultra thick] (10,0) arc [radius=5, start angle=0, end angle=180];
\node at (-0.3,0) {\textbf{A}};
\node at (10.3,0) {\textbf{D}};
\node at (5,0) {$\bullet$};
\node at (5,-0.3) {\textbf{O}};
\node at (0,0) {$\bullet$};
\node at (10,0) {$\bullet$};
\node at (2.5,4.3) {$\bullet$};
\node at (2.5,4.7) {\textbf{B}};
\node at (7.5,4.7) {\textbf{C}};
\node at (7.5,4.3) {$\bullet$};
\end{tikzpicture}
\end{center}



