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TWEET # Untitled a guest Jul 21st, 2019 83 Never
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1. documentclass[margin=5pt, tikz]{standalone}
2. usepackage{tikz}
3. usetikzlibrary{calc}
4. usetikzlibrary{angles, quotes, babel}
5. usepackage{amsmath, amssymb}
6. begin{document}
7.
8. begin{tikzpicture}[x=1cm, y=1cm, z={(4mm,3mm)}, scale=1.5, font=small]
9. pgfmathsetmacroa{2}
10. pgfmathsetmacrob{2.5}
11. pgfmathsetmacroc{3}
12.
13. pgfmathsetmacro{r}{0.5*sqrt(a^2+b^2+c^2)} %
14.
15. pgfmathsetmacro{AC}{sqrt(a^2+b^2)} %
16. pgfmathsetmacro{PA}{0.5*AC} %
17.
18. pgfmathsetmacro{h}{sqrt(r^2-PA^2)} %
19.
20. % Pyramid
21. draw (0,0,0) coordinate[label=below:\$A\$] (A)
22. --(a,0,0) node[midway, below]{\$a\$} coordinate[label=below:\$B\$] (B)
23. --(a,0,b) node[midway,right=2mm]{\$b\$} coordinate[label=\$C\$] (C);
24.
25. draw[densely dashed] (C)--(0,0,b) coordinate[label=left:\$D\$] (D)--(A);
26. draw (A)--(0,c,0) node[midway, left]{\$c\$} coordinate[label=\$S\$] (S);
27.
28.  % Diagonals
29. draw (A)--(C);
30.  draw (\$(A)!0.5!(C)\$) coordinate coordinate[label=below:\$P\$]  (P) -- (\$(S)!0.5!(C)\$) node[midway, left]{\$h\$} coordinate[label=\$M\$] (M);
31. draw (D)--(B);
32.
33.  % Point M
34. draw (S)--(M) node[midway, above]{\$r\$} -- (C) node[midway, above]{\$r\$};
35.
36. draw[densely dashed] (D) -- (M);
37. foreach P in {A,B,C} draw (M) -- (P);
38.
39. node[anchor=north west, align=left, yshift=-7mm] at (A){\$begin{array}{l}
40. a = a ,~  b = b,~  c = c \
41. |AC| =  sqrt{a^2+b^2} = AC \
42. |PA| = 0.5 |AC| = PA \
43. h = sqrt{r^2- |PA|^2} = h  \
44. r = 0.5 sqrt{a^2+b^2+c^2} = r
45. end{array}\$
46. };
47.
48. shade[ball color = gray!40, opacity = 0.4] (M) circle[radius=5mm] node{?};
49. end{tikzpicture}
50.
51. end{document}
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