MathNet 2024-part-01 — 168 problems (EN–VI) Question 90

Let $ABCD$ be a parallelogram and let a circle $k$ pass through $A$, $C$ and meet the rays $AB$, $AD$ at $E$, $F$. If $BD$, $EF$ and the tangent at $C$ concur, show that $AC$ is a diameter of $k$.
(Adelina Chopanova)