AMC 10 2022b Problem 20

Let $ABCD$ be a rhombus with $\angle ADC = 46^\circ$. Let $E$ be the midpoint of $\overline{CD}$, and let $F$ be the point on $\overline{BE}$ such that $\overline{AF}$ is perpendicular to $\overline{BE}$. What is the degree measure of $\angle BFC$? $\textbf{(A)}\ 110 \textbf{(B)}\ 111 \textbf{(C)}\ 112 \textbf{(D)}\ 113 \textbf{(E)}\ 114$