bisectors of angles....plzz help

That is the angle bisector theorem.

An easy way to see this is by looking at the ratios of the areas of \bigtriangleup{ABD} and \bigtriangleup{ADC} in two ways.

Since the altitudes are equal, they are in the ratio of the bases i.e x:y

Again \bigtriangleup{ABD} = \frac{1}{2} c \delta \sin \frac{A}{2} and \bigtriangleup{ADC} = \frac{1}{2} b \delta \sin \frac{A}{2}

giving the ratio as c:b

This can also be proved as follows................