Two Tangent Sectors

Drawing Two Tangent Sectors

This article shows how to draw two tangent sectors in LaTeX using TikZ. The figure comes from a geometry problem about the area between two sectors inside a square, but the goal here is only to reproduce the diagram cleanly.

After testing the construction in Overleaf, the coordinates can be arranged precisely enough to make the figure look symmetric.

Step-by-Step TikZ Construction

Follow the steps below to recreate the figure.

1. Open your LaTeX editor.

2. Load the tikz and tcolorbox packages in the preamble.

\documentclass{article}
\usepackage{tikz}
\usepackage[many]{tcolorbox}

3. Define the frogbox style for the problem box.

\tcbset{
  frogbox/.style={
    enhanced,
    colback=white!25!,
    colframe=green!80!black,
    enlarge top by=5.5mm,
    overlay={
      \foreach \x in {2cm,3.5cm} {
        \begin{scope}[shift={([xshift=\x]frame.north west)}]
          \path[draw=green!65!black,fill=gray!20,line width=1mm]
            (0,0) arc (0:180:5mm);

4. Add the small black eyes to complete the decoration.

\path[fill=black] (-0.2,0) arc (0:180:1.2mm);
\end{scope}}}]}}

5. In the document body, start the question box with the following command.

\begin{tcolorbox}[frogbox,title=Calculate the area of the white region inside the red square.]

6. Now define the coordinate points and their labels.

\coordinate [label=left:$\textbf{A}$] (A) at (0, 0);
\coordinate [label=right:$\textbf{B}$] (B) at (4.5*2^0.5, 0);
\coordinate [label=right:$\textbf{C}$] (C) at (4.5*2^0.5, 4.5*2^0.5);
\coordinate [label=left:$\textbf{D}$] (D) at (0, 4.5*2^0.5);
\coordinate [label=left:$\textbf{E}$] (E) at (0,4.5);
\coordinate [label=above:$\textbf{F}$] (F) at (4.5*2^0.5-4.5, 4.5*2^0.5);
\coordinate [label=right:$\textbf{G}$] (G) at (4.5*2^0.5, 4.5*2^0.5-4.5);
\coordinate [label=below:$\textbf{H}$] (H) at (4.5,0);

At this stage the sketch will look like this.

7. Draw the first sector, AEH.

\filldraw[black,fill=blue!75] (A)--(E) node[above,pos=0.5] {} arc (90:0:4.5) -- cycle;

The result will look like this.

Then draw the second sector, CFG.

\filldraw[black,fill=blue!75] (C)--(G) node[above,pos=0.5] {} arc (270:180:4.5) -- cycle;

8. Add the dimension arrow for AH.

\draw[|{stealth}-{stealth}|]([yshift=-.6cm]A)--([yshift=-.6cm]H)
  node[below,midway,sloped]{$10$\,cm};

Add a second dimension arrow for CG.

\draw[|{latex}-{latex}|]([xshift=.6cm]C)--([xshift=.6cm]G)
  node[above,midway,sloped]{$10$\,cm};

With those steps, the diagram of two tangent sectors is complete. You can still adjust the colors, dimensions, and labels to match your own worksheet or teaching material.