I have two rays drawn with a common endpoint at A. I mark a point 3/7 of the way from A to the end of one of the rays, and label it P
. I want to draw a circular arc centered at A through P between the rays.
\documentclass{amsart}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{tikz}
\usetikzlibrary{calc,angles,positioning,intersections,quotes,decorations.markings}
\usepackage{pgfplots}
\pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}
%Three points are labeled in the Cartesian plane.
\coordinate (A) at (0,0);
\coordinate (B) at (75:3);
\coordinate (C) at ($(B) +(5,0)$);
%Two rays are drawn
\draw[name path=path_AB, -latex] (A) -- (B);
\draw[name path=path_AC, -latex] (A) -- (C);
%The four vertices are labeled.
\node at ($(A)! -2.5mm! (C)$){$A$};
\node at ($(B)! -2.5mm! (A)$){$k$};
\node at ($(C)! -2.5mm! (A)$){$\ell$};
%The circular arc centered at A starts at P.
\coordinate (P) at ($(A)!3/7!(B)$);
\draw[fill] (B') circle (1.5pt);
%An arc between the rays starting at P.
\end{tikzpicture}
\end{document}