Angle bisector theorem (external case)

There are several ways of rearranging the ratios that are the result of this theorem. While I have given the usual "textbook version" I have also quoted the one that I find easiest to visualise.

I have included a proof below.

The converse of this theorem is also true.

To download this Geogebra file click here.

To download this Geogebra file click here.