KöMaL 2005 B3819

Show that if $A_1 B_1$, $A_2 B_2$ and $A_3 B_3$ are three parallel chords of a circle, then the perpendiculars dropped from the point $A_1$, $A_2$ and $A_3$ onto the line $B_2 B_3$, $B_3 B_1$ and $B_1 B_2$, respectively, are concurrent.