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\begin{tikzpicture}
[+preamble]
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
[/preamble]
\pgfmathsetmacro{\tangentpoint}{sqrt(19)}%
\begin{axis}[
ticks=none,
xmin=-1.5,
xmax=1.5,
ymin=-1.5,
ymax=1.5,
axis equal,
axis lines=middle,
xlabel=$x$,
ylabel=$y$,
disabledatascaling]
\draw[solid] (0,0) circle (1);
\path [draw=none,fill=white, fill opacity = 0] (0,0) circle (1);
\draw (0,0)--(0.9,\tangentpoint/10);
\draw[domain=0.25:1.5,smooth,variable=\x,OrangeRed,thick] plot ({\x},{(-9*\tangentpoint)*\x/19+(10*\tangentpoint)/19});
\end{axis}
\end{tikzpicture}

 

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