Problem

Source: 2019 Belarusian National Olympiad 9.2

Tags: geometry, rhombus



The rhombus $ABCD$ is given. Let $E$ be one of the points of intersection of the circles $\Gamma_B$ and $\Gamma_C$, where $\Gamma_B$ is the circle centered at $B$ and passing through $C$, and $\Gamma_C$ is the circle centered at $C$ and passing through $B$. The line $ED$ intersects $\Gamma_B$ at point $F$. Find the value of angle $\angle AFB$. (S. Mazanik)