KöMaL 2026 C1909

Let $D$ denote the midpoint of arc $BC$ not containing point $A$ on the circumcircle of equilateral triangle $ABC$. Let $E$ denote the midpoint of line segment $AC$, and let $F$ denote the midpoint of line segment $BC$. a) Find the magnitude of angle $\angle EBD$ b) Let $F'$ denote the reflection of $F$ across $E$. Prove the circle with center $F'$ and radius $F'C$ passes through the midpoint of side $AB$.