ZA-SAMO 2019 Problem 3

Let $A$ , $B$ , $C$ be points on a circle whose centre is $O$ and whose radius is $1$ , such that $\angle BAC = 45^\circ$ . Lines $AC$ and $BO$ (possibly extended) intersect at $D$ , and lines $AB$ and $CO$ (possibly extended) intersect at $E$ . Prove that $BD \cdot CE = 2$ .