Question 8
Let $ABCDEF$ be a regular octahedron with lower vertex $E$, upper vertex $F$, middle slice plane $ABCD$, center $M$ and circumsphere $k$. Furthermore let $X$ be an arbitrary point within side $ABF$. The line $EX$ intersects $k$ in $E$ and $Z$ and the plane $ABCD$ in $Y$.
$$
\text{Show that } \langle EMZ \rangle = \langle EYF \rangle.
$$
$$
\text{Show that } \langle EMZ \rangle = \langle EYF \rangle.
$$