prove the following chord properties of circles: CCT chords of equal length in a circle subtend equal angles at the centre and are equidistant from the centre the perpendicular from the centre of a circle to a chord bisects the chord; con

1. Circular Logic 9 - chords of the same length
2. Circular Logic 8 - perpendicular to chord through centre
3. Circular Logic 7 - radius perpendicular to chord
4. Circular Logic 6 - radius through the midpoint of a chord