The line [math]AF[/math] is the shortest distance between the centre A and the line [math]BC[/math].
What do you notice about angle [math]\beta[/math]?
What do you notice about [math]\angle BAF[/math] and [math]\angle CAF[/math]?[br][br]
The angles at the centre are the equal.
What do you notice about lines [math]BF[/math] and [math]CF[/math]?[br][br]
The line are equal in length.
This additional line is called a perpendicular bisector, as it meets the chord at 90 degrees, and cuts both the centre angle and the chord in half.