Circles · Challenge problem

Point $P$ lies outside a circle. One line through $P$ meets the circle at $A$ and $B$, with $PA=4$ and $AB=5$. A second line through $P$ meets the circle at $D$ and $C$, with $D$ nearer to $P$ and $PD=3$. The two lines make an angle of $60^\circ$ at $P$. Find $AC\cdot BD$.