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\begin{document}

\begin{equation}
\label{first}
\left\{\begin{array}{l}(x-x_1)^2+(y-y_1)^2=R^2\\y=\tg(\alpha)(x-x_c)+y_c\end{array}\right.
\end{equation}

\begin{equation}
\label{second}
x^2-2\cdot x \cdot x_1 + x_1^2 + \left[\tg(\alpha)x-\tg(\alpha)x_c+y_c-y_1\right]^2=R^2
\end{equation}

\begin{equation}
\label{third}
x^2-2\cdot x \cdot x_1 + x_1^2+(\tg(\alpha)x)^2+2(\tg(\alpha)x)(y_c-y_1-\tg(\alpha)x_c)+(y_c-y_1-\tg(\alpha)x_c)^2=R^2
\end{equation}

\begin{equation}
\label{fourth}
x^2(1+\tg^2(\alpha))+x\left(2\tg(\alpha)(y_c-y_1-\tg(\alpha)x_c)-2x_1\right)+x_1^2+(y_c-y_1-\tg(\alpha)x_c)^2-R^2=0
\end{equation}

\begin{equation}
\label{ABC}
\left\{\begin{array}{l}
a=1+\tg^2(\alpha)\\
b=2\tg(\alpha)(y_c-y_1-\tg(\alpha)x_c)\\
c=x_1^2+(y_c-y_1-\tg(\alpha)x_c)-R^2
\end{array}\right.
\end{equation}

\end{document}