The figure shows a
triangle
ABC, D is the incenter of triangle ABC.
Point E is taken on side AC, G and F are the centers of circles
that touch BE, AC and the
circumcircle of triangle ABC. Prove that
G, D, and F are collinear.
I have used
Geometry Expressions to visualize these geometric forms and
check out a variety of conjectures. Geometry Expressions is the
world's first Interactive Symbolic Geometry System. This means:
Geometric figures can be defined by either Symbolic Constraints
or numeric locations.
You can
download Geometry Expressions
2 Free Trial. It is a fully
featured 30 day evaluation copy of the software. All
constraints, constructions and measurements are available for
you to use.
