Question: An ordered set of three points uniquely defines a circular arc, and I'd like to be able to draw that arc in TikZ. I know about the `arc` drawing command, which does the job given a radius, two angles, and one endpoint, but in order to do that I would have to calculate the radius and the angles from the other two points on the arc. I suppose I could whip up some code to do that automatically using the PGF math library, but is there a better way? Or has anyone else already made this into a package/library I could reuse?

Answer: 
Use the following code to draw the arc corresponding to the circle through (1,2), (3,4) and (2,4) and going anticlockwise from (1,2) to (2,4).

```
\documentclass[a4paper]{article}
\usepackage{tkz-euclide}
\usetkzobj{all} 
\begin{document}
\begin{tikzpicture}
\tkzDefPoint(1,2){A}\tkzDefPoint(3,4){B}\tkzDefPoint(2,4){C}
\tkzCircumCenter(A,B,C)\tkzGetPoint{O}
\tkzDrawArc(O,A)(C)
\end{tikzpicture}
\end{document}

```
Here a code with the last version 4.25. I don't completely agree with Qrrbrbirlbel's statement: With

> 
> tkz-euclide or similar solutions that uses a separated path (which
> makes it impossible to use the arc as part of a path;
> 
> 
> 

This is only partially true. There is nothing to prevent you from using `tkz-euclide` in order to get the center of the arc, to calculate the radius OA and the start and end angles. Then you can draw what you want with `TikZ` if necessary!

```
\documentclass{standalone}
\usepackage{tkz-euclide}

\begin{document}
\begin{tikzpicture}
\tkzDefPoint(1,2){A}\tkzDefPoint(3,4){B} \tkzDefPoint(2,4){C}
\tkzDefTriangleCenter[circum](A,B,C)   \tkzGetPoint{O}
\tkzDrawArc[delta=0](O,A)(C)
\tkzFillSector[green!10](O,A)(C)
\tkzDrawSector(O,A)(C)
\tkzDrawPoints(O,A,B,C)
\end{tikzpicture}
\begin{tikzpicture}
\tkzDefPoint(1,2){A}\tkzDefPoint(3,4){B} \tkzDefPoint(2,4){C}
\tkzDefTriangleCenter[circum](A,B,C)   \tkzGetPoint{O}
\tkzDrawArc[delta=0](O,C)(A)
\tkzFillSector[red!10](O,C)(A)
\tkzDrawSector(O,C)(A)
\tkzDrawPoints(O,A,B,C)
\end{tikzpicture}
\end{document}

```

[![enter image description here](https://i.stack.imgur.com/OAILh.png)](https://i.stack.imgur.com/OAILh.png)