Circle, points and intersection

Question

Can someone please explain to me how do I get these two dots (points) after I draw the circle?

How should i draw the semicircle?

Answer 1

Intersections can be determined with the library of the same name. However, this answer is more an attempt to persuade you to add minimal working examples to your questions, i.e. documents like this:

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[bullet/.style={circle,fill,inner sep=1pt}]
\node[bullet,label=left:$A$] (A) at (0,0){};
\node[bullet,label=right:$B$] (B) at (7,0){};
\node[bullet,label=above:$C$] (C) at (3.5,0){};
\node[bullet,label=left:$D$] (D) at (0,-3){};
\node[bullet,label=right:$E$] (E) at (7,-3){};
\draw (A) -- (B);
\draw[name path=D--E] (D) -- (E);
\draw[name path=circle] (C) circle (3.5cm);
\path[name intersections={of=circle and D--E,by={M,H}}];
\node[bullet,label=below:$M$] at (M){};
\node[bullet,label=below:$H$] at (H){};
\end{tikzpicture}
\end{document}

Intersections between straight lines can also be computed with the calc library.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{angles,quotes,calc}
\begin{document}
\begin{tikzpicture}
 \draw[very thick] (-4,0) -- (4,0);
 \draw[very thick,line join=bevel] (0,0) coordinate(O) 
 -- (-34:4) coordinate(A) 
 -- ({-180+34}:4) coordinate(B) -- (4,0) coordinate(C);
 \draw (10:4) arc (10:-160:4);
 \path (intersection cs:first line={(O)--(A)}, second line={(B)--(C)})
 coordinate (D);
 \pic [draw,angle radius=1cm,"$\xi$"] {angle = O--D--B};
 \pic [draw,angle radius=1.5cm,"$34^\circ$"] {angle = O--A--B};
\end{tikzpicture}
\end{document}