Question 45
Let $ABC$ be an acute triangle with $\angle BAC \gt \angle BCA$, and let $D$ be a point on side $AC$ such that $|AB| = |BD|$. Furthermore, let $F$ be a point on the circumcircle of triangle $ABC$ such that line $FD$ is perpendicular to side $BC$ and points $F, B$ lie on different sides of line $AC$. Prove that line $FB$ is perpendicular to side $AC$.