원과 선의 교차점 "경로"(II)

Question

이 답변에 따라, 원이 (1) 세 점; (2) 점과 중심?

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (2,5);
    \coordinate (C) at (4,0);
    \coordinate (D) at (6,3);
    \coordinate (E) at (4,2);

    \draw (A)--(B)--(C)--cycle (D)--(E);
\end{tikzpicture}
\end{document}

(예를 들어 (1) A, B, C를 통과하는 원과 선분 DE의 교점, (2) A를 통과하는 원과 중심 B와 선분 DE의 교점)

Answer 1

사례 (1)의 경우: 이를 바탕으로좋은 답변,

사례 (2)의 경우: 단순히 through라이브러리를 사용합니다.

\documentclass[margin=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections,through,calc}
\tikzset{circle through 3 points/.style n args={3}{%
insert path={let    \p1=($(#1)!0.5!(#2)$),
                    \p2=($(#1)!0.5!(#3)$),
                    \p3=($(#1)!0.5!(#2)!1!-90:(#2)$),
                    \p4=($(#1)!0.5!(#3)!1!90:(#3)$),
                    \p5=(intersection of \p1--\p3 and \p2--\p4)
                    in },
at={(\p5)},
circle through= {(#1)}
}}
\begin{document}

\begin{tikzpicture}
    \coordinate (A) at (0,0);
    \coordinate (B) at (2,5);
    \coordinate (C) at (4,0);
    \coordinate (D) at (6,3);
    \coordinate (E) at (4,2);
    \draw (A)--(C)node[midway,below]{(1)}--(B)--cycle;
    \path [draw, name path=line] (D)--(E);
    \node[name path=circ, circle through 3 points={A}{B}{C},draw=blue]{};
    \path [name intersections={of=circ and line, by={K}}] ;
    \node[circle,minimum size=2pt,fill=red] at(K) {};

\end{tikzpicture}
\hfill
\begin{tikzpicture}[scale=0.55]
    \coordinate (A) at (0,0);
    \coordinate (B) at (2,5);
    \coordinate (C) at (4,0);
    \coordinate (D) at (6,3);
    \coordinate (E) at (4,2);
    \draw (A)--(B)--(C)--cycle;
    \path [draw, name path=line] (D)--(E);
    \node [draw, name path=circ] at (A) [circle through=(B)] {};
    \path [name intersections={of=circ and line, by={K}}] ;
    \node[circle,minimum size=2pt,fill=red] at(K) {};
\end{tikzpicture}

\end{document}