Question 20Triangle $ABC$ has a right angle at $B,$ $AB=1,$ and $BC=2.$ The bisector of $\angle BAC$ meets $\overline{BC}$ at $D.$ What is $BD?$ $\dfrac{\sqrt3-1}{2}$$\dfrac{\sqrt5-1}{2}$$\dfrac{\sqrt5+1}{2}$$\dfrac{\sqrt6+\sqrt2}{2}$$2\sqrt3-1$
