Tangenta la cerc (nice)

[Claudiu Mindrila]

\( \left|\begin{array}{c}
\triangle ABC;\ AB<AC\\
O\in\left(BC\right),\ BO=OC\\
A^{\prime}\in\left(BC\right),\ AA^{\prime}\perp BC\\
\left\{ B^{\prime}\right\} =C\left(O,\ \frac{BC}{2}\right)\cap AB\\
\left\{ C^{\prime}\right\} =C\left(O,\ \frac{BC}{2}\right)\cap AC\\
\left\{ D\right\} =C\left(O,\ \frac{BC}{2}\right)\cap AA^{\prime}\\
\left\{ S\right\} =B^{\prime}C^{\prime}\cap BC\end{array}\right|\Longrightarrow\angle ODS=90^{\circ} \)