# ABC is a triangle,right angled at B,D is a point on AC such that ABD=45. If AC=6 and AD=2,then legth of AB is?

mycroft holmes
272 Points
5 years ago
BD is the angular bisector and so by the property of angular bisector we have

AD/CD = AB/BC. From the given info its clear that AD/CD = ½.

Hence if AB = x, then BC = 2x. Now use Pythagoras to obtain $x = \frac{6\sqrt 5}{5}$