Cercle et intersection avec un segment

Il est possible de modifier et de compiler cet exemple :

\documentclass[border=10pt]{standalone}
\usepackage{tkz-euclide}
\begin{document}
\begin{tikzpicture}
\tkzDefPoint(0,1){J}
\tkzDefPoint(0,0){O}
\tkzDrawArc[R,line width=1pt,color=red](J,2.5)(180,0)
\foreach \i in {0,-5,-10,...,-85,-90}{
  \tkzDefPoint({2.5*cosd(\i)},{1+2.5*sind(\i)}){P}
   \tkzDrawSegment[color=orange](J,P)
   \tkzInterLC[R](P,J)(O,1)
   \tkzGetPoints{M}{N}
   \tkzDrawPoints[red](N)
   }
\foreach \i in {-90,-95,...,-175,-180}{
   \tkzDefPoint({2.5*cosd(\i)},{1+2.5*sind(\i)}){P}
   \tkzDrawSegment[color=orange](J,P)
   \tkzInterLC[R](P,J)(O,1)
   \tkzGetPoints{M}{N}
   \tkzDrawPoints[red](M)
   }
\end{tikzpicture}
\end{document}