Let $ABC$ be a triangle with $\angle ABC=130$. Point $D$ on side $AC$ is the foot of the perpendicular from $B$. Points $E$ and $F$ are on sides $(AB)$ and $(BC)$ such that $DE=DF$ and $AEFC$ is cyclic. Find $\angle EDF$.
Source: Moldova EGMO TST 2022
Tags: geometry
Let $ABC$ be a triangle with $\angle ABC=130$. Point $D$ on side $AC$ is the foot of the perpendicular from $B$. Points $E$ and $F$ are on sides $(AB)$ and $(BC)$ such that $DE=DF$ and $AEFC$ is cyclic. Find $\angle EDF$.