Chord and its Perpendicular

Let's play with circles! AB is a chord of the following circle. Draw a perpendicular to this chord through one end (here it is B). Notice where it meets the circle – let's call that point C. Now, connect C with the other end of the chord (Yes! It is A). What's special about this line? Do you think this holds true for all chords? Change the positions of A , B and see.