MathNet 2023-part-05 — 191 problems (EN–VI) Question 131

Let $ABCD$ be a trapezoid with $AB \parallel CD$ and $AB + CD = AD$. Its diagonals intersect at $E$. A line passing through the point $E$ and parallel to the bases of the trapezoid cuts $AD$ at $F$. Prove that $\angle BFC = 90^\circ$.