For any triangle ABC, let AE, BF and CG be the angle bisectors (figure 5). From the angle bisector theorem, we know that AG/GB=AC/BC, BE/EC=AB/CA, and CF/FA=BC/AB. Ceva's Theorem says that (AG/GB)(BE/EC)(AF/FC)=1 if and only if the cevians are concurrent. Substituting the values, we get (AC/BC)(AB/CA)(BC/AB)=1. Therefore, the angle bisectors are concurrent.