SAT1000 - P606

Geometry Level pending

As shown above, in $\triangle ABC$ , $AB=BC=2$ , $\angle ABC = \dfrac{2\pi}{3}$ .

If $P$ is outside plane $ABC$ and point $D$ is on segment $AC$ , so that $PD=DA, PB=BA$ , then find the maximum volume of pyramid $PBCD$ .

Let $V$ denote the volume of $PBCD$ , submit $\lfloor 10000V \rfloor$ .

Have a look at my problem set: SAT 1000 problems