Angle bisector theorem (internal 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 not included a proof as it follows from the sine rule on triangles APB and APC as sin(APB) = sin(APC) and they share a common side (AP).

The converse of this theorem is also true.

To download this Geogebra file click here.