%Soit (c) le circle de diamètre [AB]
%D et C deux points de ce cercle que les deux doits (AC) et  (BD) sont sécantes en I,et les deux diots (BC) et (AD) sont sécantes en J
\documentclass{standalone}
\standaloneconfig{margin=2mm}
\usepackage{tikz}
\usetikzlibrary{intersections,calc}

\begin{document}
\begin{tikzpicture}[scale=1.5]
    % Points A, B, C, D
    \coordinate[label=above left:$A$] (A) at (-1,0);
    \coordinate[label=right:$B$] (B) at (1,0);
    \coordinate[label=above right:$C$] (C) at (45:1);
    \coordinate[label=below:$D$] (D) at (-45:1);

    % Circle with diameter AB
    \coordinate[label=above right:$O$] (O) at ($(A)!0.5!(B)$);
    \draw (O) circle (1cm);

    % Intersection points I and J
    \coordinate[label=above right:$I$] (I) at (intersection of A--C and B--D);
    \coordinate[label=above right:$J$] (J) at (intersection of B--C and A--D);

    \draw (A) -- (B);

    \draw[blue!45] ($(I)!1.2!(A)$) -- ($(A)!1.2!(I)$);
    \draw[blue!25] ($(I)!1.2!(D)$) -- ($(D)!1.2!(I)$);

    \draw[red!30] ($(J)!1.2!(C)$) -- ($(C)!1.2!(J)$);
    \draw[red!75] ($(J)!1.2!(A)$) -- ($(A)!1.2!(J)$);

    \foreach \p in {A,B,C,D,I,J,O}
        \fill (\p) circle (0.5pt);
\end{tikzpicture}
\end{document}

%Soit (c) le circle de diamètre [AB]
%D et C deux points de ce cercle que les deux doits (AC) et  (BD) sont sécantes en I,et les deux diots (BC) et (AD) sont sécantes en J
\documentclass{standalone}
\standaloneconfig{margin=2mm}
\usepackage{tikz}
\usetikzlibrary{intersections,calc}

\begin{document}
\begin{tikzpicture}[scale=1.5]
    % Points A, B, C, D
    \coordinate[label=above left:$A$] (A) at (-1,0);
    \coordinate[label=right:$B$] (B) at (1,0);
    \coordinate[label=above right:$C$] (C) at (45:1);
    \coordinate[label=below:$D$] (D) at (-45:1);

    % Circle with diameter AB
    \coordinate[label=above right:$O$] (O) at ($(A)!0.5!(B)$);
    \draw (O) circle (1cm);

    % Intersection points I and J
    \coordinate[label=above right:$I$] (I) at (intersection of A--C and B--D);
    \coordinate[label=above right:$J$] (J) at (intersection of B--C and A--D);

    \draw (A) -- (B);

    \draw[blue!45] ($(I)!1.2!(A)$) -- ($(A)!1.2!(I)$);
    \draw[blue!25] ($(I)!1.2!(D)$) -- ($(D)!1.2!(I)$);

    \draw[red!30] ($(J)!1.2!(C)$) -- ($(C)!1.2!(J)$);
    \draw[red!75] ($(J)!1.2!(A)$) -- ($(A)!1.2!(J)$);

    \foreach \p in {A,B,C,D,I,J,O}
        \fill (\p) circle (0.5pt);
\end{tikzpicture}
\end{document}