tkz-euclide, define points outside of tikzpicture

Question

Is it possible to define points in tkz-euclide outside of the tikzpicture environment?

For example I would like to have something like this exercise in elementary geometry:

Exercise:

Consider the triangle $\Delta$ defined by the points \definePoint{A,2,3}, 
\definePoint{B,10,3} and \definePoint{C,-1,4}. 
Draw the inscribed circle and the circumscribed circle of this triangle.

Solution:

\begin{tikzpicture}
% The triangle
%A,B,C are defined in the exercise above
\tkzDrawSegments(A,B B,C C,A)

% circumcircle
\tkzCircumCenter(A,B,C)\tkzGetPoint{G}
\tkzDrawPoint(G)
\tkzDrawCircle(G,A)

% incircle
\tkzDefCircle[in](A,B,C)\tkzGetPoint{I}\tkzGetLength{rIN}
\tkzDrawPoint(I)
\tkzDrawCircle[R](I,\rIN pt)

\tkzLabelPoints[below](B)
\tkzLabelPoints[below left](C)
\tkzLabelPoints[above left](A,I,G)
\end{tikzpicture}

The point is, that if I modify the coordinates of the Points A,B,C in the question, the points in the solution should be modified too.

Answer 1

I don't know any official way to do this. TikZ seems to remembers the position of nodes between pictures, but I think this is mostly an unintended side-effect of the way nodes a stored, rather than anything officially supported. Anyway, you can write

\tikz \tkzDefPoint(1,2){A};

and the position of A will be know in the next picture (or technically until a new node with name A is defined).

It might be nicer to store the point definitions in a hook and add them at the beginning of the tikzpicture, as done in the following code. That way, one doesn't have to rely on undocumented features and can use the label option of \tkzDefPoint.

\documentclass{minimal}
\usepackage{tkz-euclide}

\makeatletter
% Define a point for use in the next TkZ drawing.
%
% Takes 2 mandatory and one optional argument:
%  * The optional argument is passed as optional argument to \tkzDefPoint.
%  * The first mandatory argument is the name of the point, e.g. “A”.
%  * The second mandatory argument is the coordinates of the point (without parenthesis).
%
% The macro also adds $name = (coordinates)$ to the text.
%
% To actually add the points to a tikzpicture, you need to call \definedPoints
% at the start of the tikzpicture.
\newcommand*\definePoint[3][]{%
    \g@addto@macro\tsx@pointhook{\tkzDefPoint[#1](#3){#2}}%
    $#2=(#3)$%
}

% hook to store the points until they are used
\def\tsx@pointhook{}

% Print anything in the hook and clear in afterwards.
\newcommand\definedPoints{%
    \tsx@pointhook%
    \gdef\tsx@pointhook{}%
}
\makeatother

\begin{document}
Consider the triangle $\Delta$ defined by the points \definePoint[label=above:$A$]{A}{2,3}, 
\definePoint{B}{8,3} and \definePoint{C}{-1,-1}. 

\begin{tikzpicture}
    % The triangle
    % A,B,C are defined in the exercise above
    \definedPoints
    \tkzDrawSegments(A,B B,C C,A)
\end{tikzpicture}
\end{document}