is mathematica able to do some planar geometry plotting

Question

I am trying to use computer to show some planar geometry plots. I donot know what software can do this, or whether mathematica can produce such plots easily.

For example, I have the following plot to show. Given any triangle ABC, let AD be the line bisecting angle BAC and intersecting BC at D. Let M be the midpoint of AD. Let the circle whose diameter is AB intersects CM at F.

How to produce these plots and show the relevant labeling of the points in mma? Is it easy to do? Could someone please give an example, or give some recommendation as to what software is best suited for this purposes?

Many thanks.

Answer 1

Here you have your graph done with Geometry Expressions in two minutes. It has many nice features, including elemental geometry calculations and an interface for exporting formulas to Mathematica.

The formula in the drawing was calculated by the program.

Free to use, $79 - $99 to be able to save.

Answer 2

Here's a very quick solution using GeoGebra to the problem you described.

It is the first time I've used GeoGebra and this took me about 20mins to make - so the program is quite well made and intuitive. What's more, it can export to dynamic, java based, webpages. Here's the one for the problem you specified: TriangleCircle.

Edit

For Mathematica demonstrations, there are lots of good examples at Plane Geometry. From this page, I found other software such as Cabri Geometry and The Geometer's Sketchpad.