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how can I fix my tikz circle to do what I want

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Below is the minimal example of my code. I would like the dotted line to stay within the circle rather than overshooting it like it currently is but I am not able to figure out how this can be done.

\documentclass[paper=a4, fontsize=12pt]{scrartcl} \usepackage[T1]{fontenc} \usepackage{amsmath,amsfonts,amsthm} % Maths  \usepackage{graphicx} \usepackage{float}\usepackage{tikz}\usetikzlibrary{arrows,%                plotmarks}\begin{document} \begin{figure}[H] \centering   \begin{tikzpicture}    % Axis    \draw[thick,->,black] (-3,0)--(3,0) node[below] {$k_x$}; % x axis    \draw[thick,->,black] (0,-3)--(0,3) node[left] {$k_y$}; % y axis    \draw[black,thick] (0,0) circle (2.5cm);    \draw[ultra thick,blue,dashed] (0,0) -- (3,3);   \end{tikzpicture}\end{figure}\end{document}

circle

I would also like to place equidistant dots as the background to my circle. I have no idea where to start! Can anyone help?


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