MathNet 2024-part-04 — 168 problems (EN–VI) Question 56

Let $A$, $B$, $C$, $D$, $E$ be five different points on the circumference of a circle in that (cyclic) order. Let $F$ be the intersection of chords $BD$ and $CE$. Show that if $AB = AE = AF$ then lines $AF$ and $CD$ are perpendicular.