Tikz: especificando el radio del círculo usando dos puntos sin el paquete Euclid

Question

Defino dos puntos usando \coordinate, a y b. Entonces trato de trazarun círculo con centro en a y radio dado por ab. Hice 3 intentos, vea el código a continuación

1. un poco naif, no funciona
2. usandohttps://tex.stackexchange.com/a/58287, No funciona
3. usandohttps://tex.stackexchange.com/a/38500esto genera un círculo con un radio enorme.

¿Hay alguna manera de hacer que funcione cualquiera de los tres? Cuanto más sencillo mejor.

\documentclass{article}
\usepackage{tkz-euclide}
\usetkzobj{all}
\usetikzlibrary{calc,patterns,angles,quotes,intersections}

\makeatletter
\def\calcLength(#1,#2)#3{%
\pgfpointdiff{\pgfpointanchor{#1}{center}}%
             {\pgfpointanchor{#2}{center}}%
\pgf@xa=\pgf@x%
\pgf@ya=\pgf@y%
\FPeval\@temp@a{\pgfmath@tonumber{\pgf@xa}}%
\FPeval\@temp@b{\pgfmath@tonumber{\pgf@ya}}%
\FPeval\@temp@sum{(\@temp@a*\@temp@a+\@temp@b*\@temp@b)}%
\FProot{\FPMathLen}{\@temp@sum}{2}%
\FPround\FPMathLen\FPMathLen5\relax
\global\expandafter\edef\csname #3\endcsname{\FPMathLen}
}
\makeatother

\begin{document}

Attempt 1:

\begin{center}
\begin{tikzpicture}[]
\coordinate (a) at (0,0);
\coordinate (b) at (1.3,1.5);
\draw (a) circle (2);
\draw (a) circle ($(b)-(a)$);
\end{tikzpicture}
\end{center}

Attempt 2:

\begin{center}
\begin{tikzpicture}[]
\coordinate (a) at (0,0);
\coordinate (b) at (1.3,1.5);
\draw (a) circle (2);
% https://tex.stackexchange.com/a/58287
\draw 
  let
  \p1 = (a),
  \p2 = (b),
  \n1 = {veclen((\x2-\x1),(\y2-\y1))}
(a) circle ({\n1});
\end{tikzpicture}
\end{center}

Attempt 3:

\begin{center}
\begin{tikzpicture}[]
\coordinate (a) at (0,0);
\coordinate (b) at (1.3,1.5);
\draw (a) circle (2);
% https://tex.stackexchange.com/a/38500
\calcLength(a,b){mylen}
\draw (a) circle (\mylen);
\end{tikzpicture}
\end{center}


\end{document}

Answer 1

Una ligera modificación del primer intento funciona. El segundo también funciona si agrega lo que falta in(y es posible que desee cambiar a la sintaxis moderna circle[radius=<radius>]).

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

Attempt 1 slightly modified:

\begin{center}
\begin{tikzpicture}
\coordinate (a) at (0,0);
\coordinate (b) at (1.3,1.5);
\draw let \p1=($(b)-(a)$),\n1={veclen(\x1,\y1)} in (a) circle[radius=\n1] ;
\end{tikzpicture}
\end{center}


\begin{center}
\begin{tikzpicture}[]
\coordinate (a) at (0,0);
\coordinate (b) at (1.3,1.5);
% https://tex.stackexchange.com/a/58287
\draw 
  let
  \p1 = (a),
  \p2 = (b),
  \n1 = {veclen((\x2-\x1),(\y2-\y1))} in 
(a) circle[radius={\n1}];
\end{tikzpicture}
\end{center}

\end{document}

Answer 2

Con tikzlibrary through, se puede hacer fácilmente:

\node [draw] at (a) [circle through={(b)}] {};

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{through}
\begin{document}
\begin{tikzpicture}
\draw[help lines] (-2,-2) grid (2,2);
\node[circle,fill=red,inner sep=1pt] (a) at (0,0){a};
\node[circle,fill=red,inner sep=1pt] (b) at (1.3,1.5){b};

\node [draw,thick] at (a) [circle through={(b)}] {};
\end{tikzpicture}
\end{document}