Tikz. Problema al crear una línea perpendicular a una línea arbitraria

Question

Me cuesta mucho dibujar una línea perpendicular al radio de un círculo. No encuentro el mismo problema si dibujo una línea perpendicular al mismo radio pero en el otro lado de la línea. Necesito que ambas líneas sean perpendiculares al mismo radio.

\documentclass[tikz,border=12pt]{standalone}
\usepackage{amsmath}
\usepackage{tikz}
\usetikzlibrary{angles,calc,math}

\begin{document}

\begin{tikzpicture}[>=stealth]
\coordinate (O) at (0,0);
\coordinate (P) at ($ ({2*cos(60)},{2*sin(60)}) $);
\draw[draw=black, fill opacity=0.2, text opacity=1] (O) circle (2);
\draw [black] (O) -- (P) coordinate (line2) node [midway, left] {$r$};
\draw [->,black] (P) -- ($(P)!1.5cm!-90:(line2)$) node [midway, right] {not perpendicular};
\draw [->,black] (O) -- ($(O)!1.5cm!-90:(line2)$) node [right] {perpendicular};
\end{tikzpicture}

\end{document}

Answer 1

¡Bienvenido! line2y Pcoincidir. Quieres definir line2de tal manera que haya una distancia hasta P.

\documentclass[tikz,border=12pt]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[>=stealth]
\coordinate (O) at (0,0);
\coordinate (P) at (60:2);
\draw[draw=black, fill opacity=0.2, text opacity=1] (O) circle[radius=2cm];
\draw [black] (O) -- (P) coordinate[pos=0.5] (line2) node [midway, left] {$r$};
\draw [->,black] (P) -- ($(P)!1.5cm!90:(line2)$) node [right] {perpendicular};
\draw [->,black] (O) -- ($(O)!1.5cm!-90:(line2)$) node [right] {perpendicular};
\end{tikzpicture}
\end{document}

O se puede poner la coordenada antes (P), en cuyo caso podemos eliminarla pos=0.5y, como amablemente sugiere @frougon, cambiar el nombre de la coordenada.

\documentclass[tikz,border=12pt]{standalone}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[>=stealth]
\coordinate (O) at (0,0);
\coordinate (P) at (60:2);
\draw[draw=black, fill opacity=0.2, text opacity=1] (O) circle[radius=2cm];
\draw [black] (O) -- coordinate(OP) (P)  node [midway, left] {$r$};
\draw [->,black] (P) -- ($(P)!1.5cm!90:(OP)$) node [right] {perpendicular};
\draw [->,black] (O) -- ($(O)!1.5cm!-90:(OP)$) node [right] {perpendicular};
\end{tikzpicture}
\end{document}

Answer 2

[turn]es otra manera.

PD: me gusta escribircódigo limpio. Por eso no corregí el código de OP.

\documentclass[tikz,border=12pt]{standalone}
\begin{document}
\begin{tikzpicture}
\path 
(0,0) coordinate (O) (60:2) coordinate (P)
(O)--(P)--([turn]-90:1.5) coordinate (M) node[right] {$M$}
(P)--(O)--([turn]90:1.5) coordinate (N) node[right] {$N$};
\draw (P)--(O) node[midway,left] {$r$} circle(2); 
\draw[->] (P)--(M); \draw[->] (O)--(N);
\end{tikzpicture}
\end{document}

Answer 3

\documentclass{standalone} 
\usepackage{tkz-euclide}
\begin{document} 
\begin{tikzpicture}[thick]
\tkzDefPoint(0,0){A}
\tkzDefPoint({2*cosd(60)},{2*sind(60)}){P}
\tkzDrawCircle(A,P)
\tkzDefPointWith[orthogonal](A,P) 
\tkzDrawLine(A,tkzPointResult)
\tkzDefPointWith[orthogonal](P,A) 
\tkzDrawLine[add=1 and 0](P,tkzPointResult)
\tkzDrawSegment(A,P)
\end{tikzpicture}
\end{document}

Avec un point aléatoirement choisi

\documentclass{standalone} 
\usepackage{tkz-euclide}
\begin{document} 
\begin{tikzpicture}
\tkzDefPoints{1/0/A}
\tkzDefRandPointOn[circle = center A radius 1 cm]
\tkzGetPoint{B}
\tkzDefPointWith[orthogonal](A,B)
\tkzDrawSegment(A,tkzPointResult)
\tkzDrawCircle(A,B)
\tkzDrawLine(A,tkzPointResult)
\tkzDefPointWith[orthogonal](B,A) \tkzGetPoint{b}
\tkzDrawLine[add=1 and 0](B,tkzPointResult)
\tkzDrawSegment(A,B)
\tkzMarkRightAngle[fill=gray!30,opacity=.6](A,B,b)
\end{tikzpicture}
\end{document}

Answer 4

De otra manera

\documentclass[tikz,border=12pt]{standalone}
\begin{document}
\begin{tikzpicture}[>=stealth,declare function={R=2;k=-2;m=5/4;myangle=60;}] 
\path 
(0,0) coordinate (O)
({R*sin(myangle)},{R*cos(myangle)}) coordinate (P)
({R*sin(myangle) + k*R*cos(myangle)},{R*cos(myangle) - k*R*sin(myangle)} ) coordinate (Q);
 \draw (O)  circle[radius=R]; 
\draw[->] (P) -- (Q);
\draw[->] (O) -- ({m*R*cos(myangle)},- {m*R*sin(myangle)} );
\draw (P) -- (O) node[midway,left] {$r$}; 
\foreach \p in {O,P}
\draw[fill=black] (\p) circle (1.5pt);
\foreach \p/\g in {O/180,P/40}
\path (\p)+(\g:3mm) node{$\p$};
\end{tikzpicture}
\end{document}