Name of theorem in plane, Euclidean Geometry regarding a circle circumscribing a triangle

Question

$\triangle{ABC}$ is circumscribed by a circle of radius $R$. If the length of $\overline{BC}$ is $a$, \begin{equation*} a = 2R\sin{A} . \end{equation*} Does this theorem have a name? (I will respond to my own post with the code to a diagram illustrating this.)

Answer 1

Here is the code for a diagram illustrating the theorem in my post.

\documentclass{amsart}

\usepackage{tikz} \usetikzlibrary{calc,intersections}

\begin{document}

\noindent \hspace*{\fill} \begin{tikzpicture}

%Triangle ABC has sides of lengths 3, 2 + 6/7, and 1 + 6/7. A = (-1,0), B = (2,0), and C = (9/7,12/7). %(The figure is magnified by 3/2.) \coordinate (A) at ({(3/2)*(-1)},0); \coordinate (B) at ({(3/2)*2},0); \coordinate (C) at ({(3/2)*9/7},{(3/2)*12/7}); % \draw (A) -- (B) -- (C) -- cycle; % \node[anchor=north, inner sep=0, font=\footnotesize] at ($(A) +(0,-0.15)$){\textit{A}}; \node[anchor=north, inner sep=0, font=\footnotesize] at ($(B) +(0,-0.15)$){\textit{B}};

%The center of the circle circumscribing the triangle is located. The radius of the circumscribing circle %is 65/42. \path[name path=a_path_to_locate_center_of_circle] ({(3/2)*1/2},0) -- ({(3/2)*1/2},2); \path[name path=another_path_to_locate_center_of_circle] ($(A)!0.5!(C)$) -- ($($(A)!0.5!(C)$)!1!90:(A)$); \coordinate[name intersections={of=a_path_to_locate_center_of_circle and another_path_to_locate_center_of_circle, by={center_of_circle}}]; % \draw[blue] let \p1=($(A)-(center_of_circle)$), \n1={atan(\y1/\x1)}, \p2=($(B)-(center_of_circle)$), \n2={atan(\y2/\x2)} in (A) arc ({\n1+180}:\n2:{(3/2)*65/42});

%Vertex C is labeled. \path let \p1=($(C)-(center_of_circle)$), \n1={atan(\y1/\x1)} in node[anchor={\n1+180}, inner sep=0, font=\footnotesize] at ($(C) +({\n1}:0.15)$){\textit{C}};

%The length of side BC is labeled "a." \path let \p1=($(B)-(C)$), \n1={atan(\y1/\x1)} in node[anchor={\n1-90}, inner sep=0, font=\footnotesize] at ($($(B)!0.5!(C)$) +({\n1+90}:0.1)$){\textit{a}};

\end{tikzpicture} \hspace{\fill}

\end{document}