Perpendicular Bisectors of Chords

Point A is the centre of the circle.[br]The line connecting points B and C is a chord in the circle. [br]A line that is perpencicular to the chord and passing through the centre of the circle is drawn.[br]Drag the points around to change the chord's length and location.[br]Notice the length of BD and CD (the line segments created by intersecting the chord).[br][br]What is ALWAYS true about where the perpendicular line intersects the chord?
Chord Bisector Demo

Information: Perpendicular Bisectors of Chords