Question 43
Let $ABC$ be a triangle with $|AC|=2|AB|$, and let $O$ be its circumcentre. Let $D$ be the intersection of the bisector of $\angle A$ with $BC$. Let $E$ be the perpendicular projection of $O$ onto $AD$, and let $F\ne D$ be the point on $AD$ such that $|CD|=|CF|$. Prove $\angle EBF=\angle ECF$.
