1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
|
\input{preamble-standalone.ltx}
\begin{document}
% Ex. No. 212 (Section 29.2.13 : "The" Circle of APOLLONIUS)
\begin{tikzpicture}[scale=.5]
\tkzDefPoints{0/0/A,6/0/B,0.8/4/C}
\tkzDefTriangleCenter[euler](A,B,C) \tkzGetPoint{N}
\tkzDefTriangleCenter[circum](A,B,C) \tkzGetPoint{O}
\tkzDefTriangleCenter[lemoine](A,B,C) \tkzGetPoint{K}
\tkzDefTriangleCenter[spieker](A,B,C) \tkzGetPoint{Sp}
\tkzDefExCircle(A,B,C) \tkzGetPoint{Jb}
\tkzDefExCircle(C,A,B) \tkzGetPoint{Ja}
\tkzDefExCircle(B,C,A) \tkzGetPoint{Jc}
\tkzDefPointBy[projection=onto B--C ](Jc) \tkzGetPoint{Xc}
\tkzDefPointBy[projection=onto B--C ](Jb) \tkzGetPoint{Xb}
\tkzDefPointBy[projection=onto A--B ](Ja) \tkzGetPoint{Za}
\tkzDefPointBy[projection=onto A--B ](Jb) \tkzGetPoint{Zb}
\tkzDefLine[parallel=through Xc](A,C) \tkzGetPoint{X'c}
\tkzDefLine[parallel=through Xb](A,B) \tkzGetPoint{X'b}
\tkzDefLine[parallel=through Za](C,A) \tkzGetPoint{Z'a}
\tkzDefLine[parallel=through Zb](C,B) \tkzGetPoint{Z'b}
\tkzInterLL(Xc,X'c)(A,B) \tkzGetPoint{B'}
\tkzInterLL(Xb,X'b)(A,C) \tkzGetPoint{C'}
\tkzInterLL(Za,Z'a)(C,B) \tkzGetPoint{A''}
\tkzInterLL(Zb,Z'b)(C,A) \tkzGetPoint{B''}
\tkzDefPointBy[reflection= over Jc--Jb](B') \tkzGetPoint{Ca}
\tkzDefPointBy[reflection= over Jc--Jb](C') \tkzGetPoint{Ba}
\tkzDefPointBy[reflection= over Ja--Jb](A'')\tkzGetPoint{Bc}
\tkzDefPointBy[reflection= over Ja--Jb](B'')\tkzGetPoint{Ac}
\tkzDefCircle[circum](Ac,Ca,Ba) \tkzGetPoint{Q}
\tkzDrawCircle[circum](Ac,Ca,Ba)
\tkzDefPointWith[linear,K=1.1](Q,Ac) \tkzGetPoint{nAc}
\tkzClipCircle[through](Q,nAc)
\tkzDrawLines[add=1.5 and 1.5,dashed](A,B B,C A,C)
\tkzDrawPolygon[color=blue](A,B,C)
\tkzDrawPolygon[dashed,color=blue](Ja,Jb,Jc)
\tkzDrawCircles[ex](A,B,C B,C,A C,A,B)
\tkzDrawLines[add=0 and 0,dashed](Ca,Bc B,Za A,Ba B',C')
\tkzDrawLine[add=1 and 1,dashed](Xb,Xc)
\tkzDrawLine[add=7 and 3,blue](O,K)
\tkzDrawLine[add=8 and 15,red](N,Sp)
\tkzDrawLines[add=10 and 10](K,O N,Sp)
\tkzDrawSegments(Ba,Ca Bc,Ac)
\tkzDrawPoints(A,B,C,N,Ja,Jb,Jc,Xb,Xc,B',C',Za,Zb,Ba,Ca,Bc,Ac,Q,Sp,K,O)
\tkzLabelPoints(A,B,C,N,Ja,Jb,Jc,Xb,Xc,B',C',Za,Zb,Ba,Ca,Bc,Ac,Q,Sp)
\tkzLabelPoints[above](K,O)
\end{tikzpicture}
\end{document}
|