Math & Science ⇒ Fill in Triangle + cool arrows with text

[3LeftsAndHome]

Ok so I am trying to emulate Figure 3 from http://www.math.siu.edu/kocik/papers/metaptolemiana.pdf which is located on page 2 of the .pdf

here is what I have gotten so far:

Code: Select all

\documentclass[12pt]{amsart}
\usepackage{fullpage}
\usepackage{amsmath,tikz,geometry,amsthm}
\usepackage{amssymb}
\usetikzlibrary{calc,intersections}

\begin{document}
    \begin{center}
    \begin{tikzpicture}[bullet/.style={coordinate,after node path={(\tikzlastnode) node {$\scriptstyle \bullet$}}}, scale = 2]
    \draw [densely dotted,black] (0,0) circle (1cm);
    \coordinate[label=below left:$A$] (A) at (-.87,-.5);
    \coordinate[label=below right:$B$] (B) at (.87,-.5);
    \coordinate[label=above:$C$] (C) at (.3,.95);
        \coordinate[label=below:$\bar{C}$] (Cbar) at (.3,-.95);
        
    \draw [thick,black] (A) -- (C) -- (B) -- cycle;
    
    \path[name path=alta] (A) -- ($(B)!(A)!(C)$);
    \path[name path=altb] (B) -- ($(A)!(B)!(C)$);


\draw[black] (-.15,0) node {\tiny $O$};
\draw[black] (.389,.1) node {\tiny $H$};
\draw[black] (.148,-.4) node {\tiny $C_F$};
\fill [black] (0,0) circle (1pt);
\fill [black] (.3,.95) circle (1pt);
\fill [black] (.3,-.95) circle (1pt);
\fill [black] ($(A)!(C)!(B)$) circle (1pt);


\draw[dotted,black] ($(A)!(C)!(B)$) -- (0,-0.5);
        \fill [black,name intersections={of=alta and altb}]
      (intersection-1) circle (1pt);
   
  \draw [dotted,black] (.3, -.95) -- (C);
  \draw [line width = 1pt,black] (C) -- ($(A)!(C)!(B)$);
  \draw [semithick,black] (A) -- ($(B)!(A)!(C)$);
  \draw [semithick,black]  (B) -- ($(A)!(B)!(C)$);
    \end{tikzpicture}
    \end{center}
\end{document}

I just cannot figure out how to fill in the triangle with grey (which should be trivial), and the cool arrow curvy lines with text is what I really am interested in. If this is all basic knowledge I apologize, but could you link me to somewhere to find more information on my problem or post some quick/blunt help. Thank you so much.

[3LeftsAndHome]

I figured it out after quite a bit of trial and error from some random example I found on the net. Here is my final copy if anyone every comes across this and needs some basic arrows

Code: Select all

 \begin{tikzpicture}[>=latex',
    ref lines/.style={thin, blue!60},
    ref points/.style={circle, black, opacity=0.7, fill, minimum size= 3pt, inner sep=0},
    every node/.style={font=\footnotesize},
    bode lines/.style={very thick, blue},
    Gclabel/.style={text=blue}, scale = 2]%[bullet/.style={coordinate,after node path={(\tikzlastnode) node {$\scriptstyle \bullet$}}}, Gclabel/.style={text=blue}, ref points/.style={circle, black, opacity=0.7, fill, minimum size= 3pt, inner sep=0}, scale = 2]

% Labels for altitudes
\begin{scope}[]
\node (KDG)  [Gclabel, black!60, text=black, draw]
    at (1, .9) {$ear$};
\draw (KDG.west) edge [->, shorten >=1pt, semithick, black, bend right = 8] 
    (.3, .4);
    
    \node (KDGa)  [Gclabel, black!60, text=black, draw]
    at (1.4, 0) {$stem$};
\draw (KDGa.west) edge [->, shorten >=1pt, semithick, black, bend right = 8] 
    (.3, -.35);
    
        \node (KDGa)  [Gclabel, black!60, text=black, draw]
    at (1.4, -.8) {$root$};
\draw (KDGa.west) edge [->, shorten >=1pt, semithick, black, bend left = 8] 
    (.3, -.7);
    
    \node (KDGa)  [Gclabel, black!60, text=black, draw]
    at (-1, -1) {$foot$};
\draw (KDGa.east) edge [->, shorten >=1pt, semithick, black, bend right = 12] 
    (0.28, -.52);
\end{scope}

\draw [densely dotted,black] (0,0) circle (1cm);
    \coordinate[label=below left:$A$] (A) at (-.87,-.5);
    \coordinate[label=below right:$B$] (B) at (.87,-.5);
    \coordinate[label=above:$C$] (C) at (.3,.95);
        \coordinate[label=below:$\bar{C}$] (Cbar) at (.3,-.95);
        
    \draw [thin,black] (A) -- (C) -- (B) -- cycle;
    
\filldraw[fill=gray, opacity=.25] (A) -- (C) -- (B) -- cycle;

    
    \path[name path=alta] (A) -- ($(B)!(A)!(C)$);
    \path[name path=altb] (B) -- ($(A)!(B)!(C)$);


\draw[black] (-.15,0) node {\tiny $O$};
\draw[black] (.389,.1) node {\tiny $H$};
\draw[black] (.148,-.4) node {\tiny $C_F$};
\fill [black] (0,0) circle (1pt);
\fill [black] (.3,.95) circle (1pt);
\fill [black] (.3,-.95) circle (1pt);
\fill [black] ($(A)!(C)!(B)$) circle (1pt);

       \fill [black,name intersections={of=alta and altb}]
      (intersection-1) circle (1pt);
   
  \draw [dotted,black] (.3, -.95) -- (C);
  \draw [line width = 1.2pt,black] (C) -- ($(A)!(C)!(B)$);
  \draw [thin,black] (A) -- ($(B)!(A)!(C)$);
  \draw [thin,black]  (B) -- ($(A)!(B)!(C)$);
  
    \end{tikzpicture}