Euclidean geometry; concyclic points and parallelism problem.

Question

Given an acute triangle $ABC$ with a tangent to its circle at point $B$. If $E$ is the foot of the perpendicular from $B$ to $AC$ and $F$ is the foot of the perpendicular of $C$ to the tangent line. Show that $EF$ is parallel to $AB$.

Answer 1

Consider arc $AB$, then angle $ACB$ is equal to angle $ABD$