Geometric constructions with tikz

Question

Is it possible to do basic geometric using tikz like angle bisectors, bisection of line segments, inscribed circles, circumscribed circles etc.? More in detail I want a command which takes three points (not on one line) as argument and gives me the (inscribed) circumscribed circle of the triangle defined by this points. Analogously I want a command which takes two points and gives me the bisection of the line segment defined by those points, similar in the case of angle bisection.

Answer 1

tkz-euclide provides commands for many geometric constructions. It is available on Altermundus' site and CTAN. The manual is quite good (except that the command tkzDrawPolygon used in many examples doesn't exist), but only available in French (though even if you don't speak French, you should be able to figure everything out from the examples). I have never used it before, but was able to draw the following in a few minutes:

\documentclass{article}
\usepackage{tkz-euclide}
\begin{document}

\begin{tikzpicture}
    % The triangle
    \tkzDefPoint(2,2){A}
    \tkzDefPoint(5,-2){B}
    \tkzDefPoint(1,-2){C}
    \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}
\end{document}