CN-LEAGUE 2008 Problem 1

Given a convex quadrilateral with $\angle B+\angle D<180$ .Let $P$ be an arbitrary point on the plane,define $f(P)=PA*BC+PD*CA+PC*AB$ . (1)Prove that $P,A,B,C$ are concyclic when $f(P)$ attains its minimum. (2)Suppose that $E$ is a point on the minor arc $AB$ of the circumcircle $O$ of $ABC$ ,such that $AE=\frac{\sqrt 3}{2}AB,BC=(\sqrt 3-1)EC,\angle ECA=2\angle ECB$ .Knowing that $DA,DC$ are tangent to circle $O$ , $AC=\sqrt 2$ ,find the minimum of $f(P)$ .