Question 90
Let $AA'$, $BB'$, $CC'$ be the altitudes from the vertices of an acute-angled triangle $ABC$. Points $E$ and $F$ lie on the segments $CB'$ and $BC'$ respectively, such that
$$
B'E \cdot C'F = BF \cdot CE.
$$
Prove that the quadrilateral $AEA'F$ is cyclic.
$$
B'E \cdot C'F = BF \cdot CE.
$$
Prove that the quadrilateral $AEA'F$ is cyclic.