mjhjmtu

Is it possible to have a macro which uses the length between to points to calculate another calculate, as in the following example:

documentclass[tikz,border=10pt]standalone
usepackagetikz
usetikzlibrarycalc
begindocument 

begintikzpicture
 coordinate (A) at (0,0);
 coordinate (B) at (2,5);
 coordinate (C) at (7,0);

 % Is this possible?
 % From point C to the direction of point A with the length of
 % from point A to point B
 % coordinate (D) at ($(C)!(A)!(A)-(B)$);
 % or
 % From point C to the direction of 60 degrees with the length of
 % from point A to point B
 % coordinate (D) at ($(C)!(60)!(A)-(B)$);

 draw (A)--(B)--(C)--cycle;
endtikzpicture

enddocument

Something like this?

documentclass[tikz,border=10pt]standalone
usetikzlibrarycalc
begindocument 

begintikzpicture
 coordinate (A) at (0,0);
 coordinate (B) at (2,5);
 coordinate (C) at (7,0);

 % Is this possible?
 % From point C to the direction of point A with the length of
 % from point A to point B
 path let p1=($(B)-(A)$),n1=veclen(x1,y1) in ($(C)!n1!(A)$)
 coordinate(D) ($(C)+(60:n1)$) coordinate (D');
 % or
 % From point C to the direction of 60 degrees with the length of
 % from point A to point B
 % coordinate (D) at ($(C)!(60)!(A)-(B)$);

 draw (A)--(B)--(C)--cycle;
 draw[blue,thick] (C) -- (D);
 draw[red,thick] (C) -- (D');
endtikzpicture

enddocument

Or with styles:

documentclass[tikz,border=10pt]standalone
usetikzlibrarycalc
begindocument 

begintikzpicture[towards/.style args=#1 from #2 with length from #3 to #4%
insert path=let p1=($(#3)-(#4)$),n1=veclen(x1,y1) in
($(#2)!n1!(#1)$),into direction/.style args=#1 from #2 with length from #3 to #4%
insert path=let p1=($(#3)-(#4)$),n1=veclen(x1,y1) in
($(#2)+(#1:n1)$)]
 coordinate (A) at (0,0);
 coordinate (B) at (2,5);
 coordinate (C) at (7,0);

 % Is this possible?
 % From point C to the direction of point A with the length of
 % from point A to point B
 path[towards=A from C with length from A to B] 
 coordinate(D) ;
 % or
 % From point C to the direction of 60 degrees with the length of
 % from point A to point B
 % coordinate (D) at ($(C)!(60)!(A)-(B)$);
 path[into direction=60 from C with length from A to B] 
 coordinate(D') ;

 draw (A)--(B)--(C)--cycle;
 draw[blue,thick] (C) -- (D);
 draw[red,thick] (C) -- (D');
endtikzpicture
enddocument