Bisector of chord in a circle

[size=150][b]Task:[/b] [color=#980000]WITHOUT[/color] checking off either of the checkboxes below, make a conjecture on the property of the bisector of a chord ([b]BC[/b]) passing through the centre ([b]O[/b]) of a circle. Move the points around, change the radius does any of this make a difference?[br][br]Now select the checkboxes.[br][br][list][*]Was your conjecture correct?[/*][*]What would the proof of this look like?[/*][/list][/size]

Information: Bisector of chord in a circle