[TikZ] Tiếp tuyến chung của hai đường tròn

Hình vẽ sau minh họa tiếp tuyến trong chua của hai đường tròn $(P,R)$ và $(Q,r)$

$$ \begin{tikzpicture} \pgfmathsetmacro{\b}{75} \pgfmathsetmacro{\a}{15} \pgfmathsetmacro{\R}{2} \pgfmathsetmacro{\r}{1} \pgfmathsetmacro{\P}{\R*tan(\b)} \pgfmathsetmacro{\Q}{\R/cos(\b)} \pgfmathsetmacro{\p}{\r/tan(\a)} \pgfmathsetmacro{\q}{\r/sin(\a)} \draw (0,0) circle (\R) ; \fill[left color=gray!80, right color=gray!60, middle color=white] (0,0) circle (\R) ; \draw[thick, white] (0,0) circle (.8*\R); \shade[ball color=white] (0,0) circle (.3) node[left,xshift=-5] {$P$}; \draw (\Q+\q-.3, 0) circle (\r); \fill[left color=gray!80, right color=gray!60, middle color=white] (\Q+\q-.3, 0) circle (\r) ; \draw[thick, white] (\Q+\q-.3,0) circle (.8*\r); \shade[ball color=white] (\Q+\q-.3,0) circle (.15) node[right, xshift=2] {$Q$}; \begin{scope}[ultra thick] \draw (\b:\R) arc (\b:360-\b:\R) ; \draw (\b:\R) -- ( \P, 0 ); \draw (-\b:\R) -- ( \P, 0 ); \draw (\Q-.3,0) -- + (\a:\p) arc (105:-105:\r) ; \draw (\Q-.3,0) -- + (-\a:\p); %\draw (\b:\R) arc (\b:360-\b:\r) ; \end{scope} \draw (0,0) -- (\b:\R) node[midway, above,sloped] {$R$} node[above] {$A$}; \draw (-\b:\R)--(0,0) ; \draw (\Q+\q-.3,0) -- +(105:\r) node[midway,above, sloped] {$r$} node[above] {$E$}; \draw (\Q+\q-.3,0) -- +(-105:\r) node[below] {$D$}; \node[below] at (-\b:\R) {$B$}; \node[below] at (\Q-.3,0) {$C$}; \draw[dash pattern=on5pt off3pt] (0,0) -- (\Q+\q-.3,0); \node[fill=white] at (0.73*\Q, 0) {$\theta$} ; \draw (\Q-1.8,0) arc (180:195:1.5); \draw (\Q-1.8,0) arc (180:165:1.5); \end{tikzpicture} $$

\begin{tikzpicture}
\pgfmathsetmacro{\b}{75}
\pgfmathsetmacro{\a}{15}
\pgfmathsetmacro{\R}{2}
\pgfmathsetmacro{\r}{1}
\pgfmathsetmacro{\P}{\R*tan(\b)}
\pgfmathsetmacro{\Q}{\R/cos(\b)}
\pgfmathsetmacro{\p}{\r/tan(\a)}
\pgfmathsetmacro{\q}{\r/sin(\a)}
\draw (0,0) circle (\R) ;
\fill[left color=gray!80, right color=gray!60, middle
color=white] (0,0) circle (\R) ;
\draw[thick, white] (0,0) circle (.8*\R);
\shade[ball color=white] (0,0) circle (.3) node[left,xshift=-5] {$P$};
\draw (\Q+\q-.3, 0) circle (\r);
\fill[left color=gray!80, right color=gray!60, middle
color=white] (\Q+\q-.3, 0) circle (\r) ;
\draw[thick, white] (\Q+\q-.3,0) circle (.8*\r);
\shade[ball color=white] (\Q+\q-.3,0) circle (.15)
node[right, xshift=2] {$Q$};
\begin{scope}[ultra thick]
\draw (\b:\R) arc (\b:360-\b:\R) ;
\draw (\b:\R) -- ( \P, 0 );
\draw (-\b:\R) -- ( \P, 0 );
\draw (\Q-.3,0) -- + (\a:\p) arc (105:-105:\r) ;
\draw (\Q-.3,0) -- + (-\a:\p);
%\draw (\b:\R) arc (\b:360-\b:\r) ;
\end{scope}
\draw (0,0) -- (\b:\R) node[midway, above,sloped] {$R$} node[above] {$A$};
\draw (-\b:\R)--(0,0) ;
\draw (\Q+\q-.3,0) -- +(105:\r) node[midway,above, sloped] {$r$}
node[above] {$E$};
\draw (\Q+\q-.3,0) -- +(-105:\r) node[below] {$D$};
\node[below] at (-\b:\R) {$B$};
\node[below] at (\Q-.3,0) {$C$};
\draw[dash pattern=on5pt off3pt] (0,0) -- (\Q+\q-.3,0);
\node[fill=white] at (0.73*\Q, 0) {$\theta$} ;
\draw (\Q-1.8,0) arc (180:195:1.5);
\draw (\Q-1.8,0) arc (180:165:1.5);
\end{tikzpicture}

Huynh Cao Cuong (chia sẻ)