The following solution defines a to path arc through that expects one coordinate (including the () as it may preceeded with + or ++).

The solution provides two styles:

• arc through ccw draws a counter-clockwise arc and
• arc through cw draws a clockwise arc.

The point that is given as an argument to both styles is used to calculate the radius. The arc is not necessary drawn through this points, the circle on which the arc lies only goes to this point. This makes it possible to draw the rest of said circle without the need to give another coordinate. (The name arc on circle that goes through would probably be a better name for the styles …)

The coordinate arc through center is defined after the to path and can be used for later reference (as long as no other arc through is drawn).

\documentclass[tikz]{standalone} \makeatletter \tikzset{ @arc through/.style 2 args={ to path={ \pgfextra \pgfextract@process\pgf@tostart{\tikz@scan@one@point\pgfutil@firstofone(\tikztostart)\relax}% \pgfextract@process\pgf@tothrough{\tikz@scan@one@point\pgfutil@firstofone#1}% \pgfextract@process\pgf@totarget{\tikz@scan@one@point\pgfutil@firstofone(\tikztotarget)\relax}% \pgfextract@process\pgf@topointMidA{\pgfpointlineattime{.5}{\pgf@tostart}{\pgf@tothrough}}% \pgfextract@process\pgf@topointMidB{\pgfpointlineattime{.5}{\pgf@totarget}{\pgf@tothrough}}% \pgfextract@process\pgf@tocenter{% \pgfpointintersectionoflines{\pgf@topointMidA} {\pgfmathrotatepointaround{\pgf@tothrough}{\pgf@topointMidA}{90}} {\pgf@topointMidB}{\pgfmathrotatepointaround{\pgf@tothrough}{\pgf@topointMidB}{90}}}% \pgfcoordinate{arc through center}{\pgf@tocenter}% \pgfpointdiff{\pgf@tocenter}{\pgf@tostart}% \pgfmathveclen@{\pgfmath@tonumber\pgf@x}{\pgfmath@tonumber\pgf@y}% \edef\pgf@toradius{\pgfmathresult pt} \pgfmathanglebetweenpoints{\pgf@tocenter}{\pgf@tostart}% \let\pgf@tostartangle\pgfmathresult \pgfmathanglebetweenpoints{\pgf@tocenter}{\pgf@totarget}% \let\pgf@toendangle\pgfmathresult \ifdim\pgf@tostartangle pt>\pgf@toendangle pt\relax \pgfmathsetmacro\pgf@tostartangle{\pgf@tostartangle-360}% \fi #2%  \pgfmathsetmacro\pgf@toendangle{\pgf@toendangle-360}% \fi \endpgfextra arc [radius=+\pgf@toradius, start angle=\pgf@tostartangle, end angle=\pgf@toendangle] \tikztonodes }}, arc through ccw/.style={@arc through={#1}{\iffalse}}, arc through cw/.style={@arc through={#1}{\iftrue}}, } \makeatother \begin{document} \begin{tikzpicture} \coordinate (A) at ( 3, 1); \coordinate (B) at ( 1, 2); \coordinate (C) at (-2,-2); \draw[ultra thick, draw=blue, fill=blue!50] (A) to[arc through ccw=(B)] (C) -- (arc through center) -- cycle; \foreach \p in {A,B,C, arc through center} \fill[red] (\p) circle(2pt); \end{tikzpicture} \begin{tikzpicture} \coordinate (A) at ( 3, 1); \coordinate (B) at ( 1, 2); \coordinate (C) at (-2,-2); \draw[ultra thick, draw=green, fill=green!50] (B) to[arc through ccw=(A)] (C) -- (arc through center) -- cycle; \draw[ultra thick, draw=blue,  fill=blue!50] (B) to[arc through cw= (A)] (C) -- (arc through center) -- cycle; \foreach \p in {A,B,C, arc through center} \fill[red] (\p) circle(2pt); \end{tikzpicture} \end{document} 

The ext.topaths.arcthrough library from my tikz-extensions package has been created from this answer and provied a arc through key that expects one coordinate (including the () as it may preceeded with + or ++).

As an argument, arc through also accepts clockwise and counter clockwise (default).

The point that is given as an argument is used to calculate the radius. The arc is not necessary drawn through this point, the circle on which the arc lies goes through this point. This makes it possible to draw the rest of said circle without the need to give another coordinate. (The name arc on circle that goes through would probably be a better name for this …)

The coordinate arc through center is defined after the to path and can be used for later reference (as long as no other arc through is used again, of course).

\documentclass[tikz]{standalone} \usetikzlibrary{ext.topaths.arcthrough} \begin{document} \begin{tikzpicture} \coordinate[label=above right:$A$] (A) at ( 3, 1); \coordinate[label=above:$B$] (B) at ( 1, 2); \coordinate[label=below left:$C$]  (C) at (-2,-2);   \draw[ultra thick, draw=green, fill=green!50]  (B) to[arc through={clockwise,(A)}] (C)  -- (arc through center) -- cycle; \draw[ultra thick, draw=blue, fill=blue!50]   (B) to[arc through=(A)]  (C)  -- (arc through center) -- cycle; \foreach \p in {A,B,C, arc through center}  \fill[red] (\p) circle[radius=2pt]; \end{tikzpicture} \end{document} 

This solution uses the same calculation algorithm as the one in JLDiaz’ answer.

This solution uses the same calculation algorithm as the one in JLDiaz’ answer.