I have been drawing some pictures using tikz, and am wondering if I can name a number.

For example, I pick a point $A$ with position angle $alpha=45degree$ on a circle, and a line going through that point with direction angle $beta=alpha+90degree=135degree$ (wich is perpendicular to the position vector).

Later I change the point $A$ to be $alpha=60degree$, and then $beta=150 degree$.

Now I change both angles manually. If I can name the first angle $alpha$ and the second angle $beta$, then I only need to change $alpha$: $beta$ will vary accordingly.

Is there a way to do this, naming a number? Thanks!

You can also use tikzmath from math tikzlibrary

    documentclass[border=1cm,multi]{standalone}

usepackage{tikz}

usetikzlibrary{math,angles,quotes}



begin{document}

tikzmath{

R=2; % circle radius

d=3; % distance between A and B

a1=30; % angle alpha

a2=a1 + 90; % angle beta

}

begin{tikzpicture}

draw (0,0)circle[radius=R cm];

path (a1:R) coordinate[label=(A)] (A) +(a2:d)coordinate[label=(B)](B);

draw (A)--(B);



coordinate(O) at(0,0);

coordinate(x) at(1,0);

draw(x)--(O)--(A);

pic[draw,"(alpha=a1)",angle eccentricity=2.25]{angle=x--O--A};



end{tikzpicture}

tikzmath{

R=2; % circle radius

d=3; % distance between A and B

a1=60; % angle alpha

a2=a1 + 90; % angle beta

}

begin{tikzpicture}

draw (0,0)circle[radius=R cm];

path (a1:R) coordinate[label=(A)] (A) +(a2:d)coordinate[label=(B)](B);

draw (A)--(B);



coordinate(O) at(0,0);

coordinate(x) at(1,0);

draw(x)--(O)--(A);

pic[draw,"(alpha=a1)",angle eccentricity=2.25]{angle=x--O--A};



end{tikzpicture}

end{document}

You can use insert path in order to insert paths that are largely the same. This is illustrated in the MWE most of which is illustration.

documentclass[tikz,border=3.14mm]{standalone}

begin{document}

begin{tikzpicture}[insert points/.style={insert path={%

(#1:1) coordinate(A) (#1+90:1) coordinate(B)}}]

% with 45 degrees

path[insert points=45];

% only illustration

draw circle (1); 

foreach X in {A,B}

{node[fill,inner sep=1pt,label=right:X] at (X){};}

% second example (shifted to avoid interference)

begin{scope}[xshift=4cm]

% with 60 degrees

path[insert points=60];

% only illustration

draw circle (1);

foreach X in {A,B}

{node[fill,inner sep=1pt,label=right:X] at (X){};}

end{scope}

end{tikzpicture}

end{document}

If I understood correctly, you want to place a point A on a circle at a certain angle and then a point placed on the perpendicular to this 90 degree radius.

Then you want these two angles to be relative. It is possible to define a constant with the LaTeX macro def and to define the other one with the calc library which allows to place a point with respect to two others with a given angle (see pages 143 and 144 of the manual 3.0.1a).

Here is an example:

documentclass[tikz,border=5mm]{standalone}

usetikzlibrary{calc}

begin{document}

defalpha{45}



begin{tikzpicture}

draw (0,0)circle (2cm)circle(1pt);

draw  (alpha:2) coordinate(A)circle(1pt);

draw ($(A)!1!-90:(0,0)$)--($(A)!1!90:(0,0)$);

end{tikzpicture}



end{document}

And as a Christmas gift, a little animation:

documentclass[tikz,border=5mm]{standalone}

usetikzlibrary{calc}

begin{document}

defalpha{40}

foreach alpha in {0,5,...,180}{

begin{tikzpicture}

useasboundingbox (-3,-3) rectangle (3,3);

draw (0,0)circle (2cm)circle(1pt);

draw  (alpha:2) coordinate(A)circle(1pt);

draw ($(A)!1!-90:(0,0)$)--($(A)!1!90:(0,0)$);

end{tikzpicture}

}

end{document}

A PSTricks solution only for fun purposes.

Still image

documentclass[pstricks,12pt]{standalone}

usepackage{pst-eucl}

begin{document}

pspicture(8,8)

pstGeonode(4,4){O}([nodesep=2,angle=60]O){A}([offset=-2]{O}A){X}([offset=2]{O}A){Y}

pstCircleOA{O}{A}

psline(X)(Y)

endpspicture

end{document}

Animated

documentclass[pstricks,12pt]{standalone}

usepackage{pst-eucl}

begin{document}

foreach i in {0,30,...,330}{%

pspicture(8,8)

pstGeonode(4,4){O}([nodesep=2,angle=i]O){A}([offset=-2]{O}A){X}([offset=2]{O}A){Y}

pstCircleOA{O}{A}

psline(X)(Y)

endpspicture}

end{document}