\input{preamble-standalone.ltx} \begin{document} % Ex. No. 242 (Section 30.2.12 : "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}