Segments in a isosceles triangle

Question

In the diagram, $\triangle ABP$ is isosceles of base $AB$, $\angle APB=2\alpha$ and $\angle ACB = \alpha$.

If $PB=PD=3$ , $PD=2$, $AD\times CD= ?$

I don't see how to approach this problem, i thought i needed more information but my teacher says that it is possible.

Any hints?

Thanks.

Answer 1

If you draw a circle with center $P$ passing through $A$ and $B$, then arc $AB$ has measure $2\alpha$, so points $X$ such that $\angle AXB = \alpha$ will lie on the circle. Since $\angle ACB = \alpha$, point $C$ lies on the circle.

You should be able to take it from here.