a: \(\dfrac{AB'}{AB}=\dfrac{AC'}{AC}\)
=>\(\dfrac{AB}{AB'}=\dfrac{AC}{AC'}\)
=>\(\dfrac{AB}{AB'}-1=\dfrac{AC}{AC'}-1\)
=>\(\dfrac{AB-AB'}{AB'}=\dfrac{AC-AC'}{AC'}\)
=>\(\dfrac{BB'}{AB'}=\dfrac{CC'}{AC'}\)
=>\(\dfrac{AB'}{BB'}=\dfrac{AC'}{CC'}\)
b: \(\dfrac{AB'}{AB}=\dfrac{AC'}{AC}\)
=>\(1-\dfrac{AB'}{AB}=1-\dfrac{AC'}{AC}\)
=>\(\dfrac{AB-AB'}{AB}=\dfrac{AC-AC'}{AC}\)
=>\(\dfrac{BB'}{AB}=\dfrac{CC'}{AC}\)