Question 31
$AB$ and $CD$ are two parallel chords of a parabola. Circle $S_1$ passing through points $A$, $B$ intersects circle $S_2$ passing through $C$, $D$ at points $E$, $F$.
Prove that if $E$ belongs to the parabola, then $F$ also belongs to the parabola.
Prove that if $E$ belongs to the parabola, then $F$ also belongs to the parabola.