The vertices of a triangle are A (-1, -7 ), B ( 5, 1 ) and C (1,4). If the internal angle bisector of $\angle$B meets the side AC in D, then find the length of BD.  Solution: Let BD be the bisector of $\angle$ABC. Then, AD : DC = AB : BC and AB =         BC = ∴ AD : DC = 2 : 1 By section formula, D $\equiv$( 1/3, 1/3) Distance BD . How did they come up with the first conclusion? AD:DC=AB:BC

Its by the angle bisector theorem. The side on which the bisector lies is divided in the ratio equal to the ratio of the other 2 sides...

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