TeX - LaTeX Asked by Alejandra Benítez on January 13, 2021
documentclass{article} % or another class
usepackage{xcolor} % before tikz or tkz-euclide if necessary
usepackage{tkz-euclide} % no need to load TikZ
usepackage{multirow}
usetikzlibrary{babel} %if there are problems with the active characters
begin{document}
begin{tikzpicture}
%arbitrary points
tkzDefPoint(0,4){A}
tkzDefPoint(2,2){B}
%tangent to circle
% tkzDrawLine(A,B)%--------uncomment to show line
%mid point of tangent line
tkzDefMidPoint(B,A)tkzGetPoint{P}
%perpendicular to tangent
tkzDefLine[orthogonal =through P](B,A)tkzGetPoint{X}
tkzDrawSegment(P,X)
tkzLabelPoints(X)
%drw circle with radius XP
tkzDefCircle[through](X,P)
tkzGetLength{rXPpt}
tkzpttocm(rXPpt){rXPcm}
tkzDrawCircle(X,P)
%define radius of smaller circle
tkzDefPointWith[linear,K=0.3](X,P) tkzGetPoint{x}
tkzLabelPoints(x)
%draw smaller circle
tkzDefCircle[through](x,P)
tkzGetLength{rxPpt}
tkzpttocm(rxPpt){rxPcm}
tkzDrawCircle(x,P)
%labelling radius r1
tkzDrawPoints(X,x)
tkzDrawSegment[<->, >=triangle 45](x,P)
tkzLabelLine[pos=0.5,left](x,P){r1}
%label radius r
tkzCalcLength[cm](X,P)tkzGetLength{rXP}
tkzDefShiftPoint[X](-90:rXP){y}
tkzDrawSegments[<->, >=triangle 45](X,y)
tkzLabelLine[pos=0.5,left](X,y){r}
end{tikzpicture}
end{document}
Second Circle
The preamble for the code remains the same
begin{tikzpicture}[scale=0.55]
%arbitrary points
tkzDefPoint(6,4){A}
tkzDefPoint(6,-4){B}
%tangent to circle
%tkzDrawLine(A,B)%--------uncomment to show line
%mid point of tangent line
tkzDefMidPoint(B,A)tkzGetPoint{P}
%perpendicular to tangent
tkzDefLine[orthogonal =through P](A,B)tkzGetPoint{X}
tkzDrawSegment[<->, >=triangle 45](P,X)
tkzLabelPoints[above](X)
%drw circle with radius XP
tkzDefCircle[through](X,P)
tkzDrawCircle(X,P)
%perpendicular to tangent
tkzCalcLength[cm](X,P)tkzGetLength{rXP}
tkzDefShiftPoint[X](180:rXP*2){y}
%define radius of smaller circle
tkzDefPointWith[linear,K=0.3](y,P) tkzGetPoint{x}
tkzLabelPoints[above](x)
tkzDrawSegment[<->, >=triangle 45](P,x)
%drw circle with radius XP
tkzDefCircle[through](x,P)
tkzDrawCircle(x,P)
%label
tkzLabelLine[pos=0.5,above](x,P){r1}
tkzCalcLength[cm](X,P)tkzGetLength{rXP}
tkzDefShiftPoint[X](-60:rXP){X'}
tkzDrawSegments[<->, >=triangle 45](X,X')
tkzLabelLine[pos=0.5,above, sloped](X,X'){r}
tkzDrawPoints(X,x)
end{tikzpicture}
Correct answer by js bibra on January 13, 2021
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