Question 87
Let $\Gamma$ be a circle with center $O$ and $A E$ be a diameter. Point $D$ lies on segment $O E$ and point $B$ is the midpoint of one of the $\operatorname{arcs} \widehat{A E}$ of $\Gamma$. Construct point $C$ such that $A B C D$ is a parallelogram. Lines $E B$ and $C D$ meet at $F$. Line $O F$ meets the minor $\operatorname{arc} \widehat{E B}$ at $I$. Prove that $E I$ bisects $\angle B E C$.
Supplemental illustration (AI-generated; one example, not to infer additional assumptions).
Supplemental illustration (AI-generated; one example, not to infer additional assumptions).