`\draw (x,y) arc (start:stop:radius);`

draws an arc

- with radius
`radius`

- starts from
`(x,y)`

- with center
`(x-r*cos(start), y-r*sin(start))`

and
- ends at
`(x-r*cos(start)+r*cos(stop), y-r*sin(start)+r*sin(stop))`

.

For example,

```
\draw[red] (0,0) arc (30:60:3);
```

draws an arc

- of radius
`3`

- starting from
`(0,0)`

- with center
`(0-3*cos(30),0-3*sin(30))`

and
- ending at
`(0-3*cos(30)+3*cos(60),0-3*sin(30)+3*sin(60))`

.

```
\draw[blue] (0,0) -- ++(30+180:3) -- +(60:3);
```

draw a blue line to the arc to make a complete sector as shown in the following figure.

## Minimal Working Example

```
\documentclass[tikz,border=12pt]{standalone}
\begin{document}
\foreach \start/\stop in {30/60,45/90,135/180,0/180,45/315}
{
\begin{tikzpicture}
\draw[lightgray,ultra thin] (-6,-6) grid (6,6);
\draw[red] (0,0) arc (\start:\stop:3);
\draw[blue] (0,0) -- ++(\start+180:3) -- +(\stop:3);
\node[anchor=north] at (0,6) {$(\start:\stop:3)$};
\end{tikzpicture}
}
\end{document}
```

## Other outputs for you to analyze

A solution which allows to draw `intersection segments`

of any two intersections is available as tikz library `fillbetween`

.

This library works as general purpose `tikz`

library, but it is shipped with `pgfplots`

and you need to load `pgfplots`

in order to make it work:

```
\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}
\begin{document}
\begin{tikzpicture}
\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);
% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];
\end{tikzpicture}
\end{document}
```

The key `intersection segments`

is described in all detail in the `pgfplots`

reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path `temp1`

which is the first intersection segment of `red and blue`

, more precisely, it is the first intersection segment in the `L`

eft argument in `red and blue`

: `red`

. This path is drawn as thin black path. Substitute its `\draw`

statement by `\path`

to make it invisible.

Compute the desired `intersection segment`

by intersecting `temp1`

and `green`

and use the correct intersection segment. By trial and error I figured that it is the third segment of path `temp1`

which is written as `L3`

(`L`

= left argument in `temp1 and green`

and `3`

means third segment of that path).

The argument involves some trial and error because `fillbetween`

is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an `intersection segment`

should be the continuation of another path, use `--`

as before the first argument in sequence. This allows to fill paths segments:

```
\documentclass{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}
\begin{document}
\begin{tikzpicture}
\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);
% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]
[intersection segments={of=temp1 and green, sequence={--R2}}]
;
\end{tikzpicture}
\end{document}
```

## Best Answer

If people come to this question via Google (like me) and want to get only a rectangle with rounded corners:

This is an empty rectangle with rounded corners. The rectangle is from

`(0, 0)`

- the lower left corner - to`(4, 1)`

- the upper right corner.