If two equal chords of a circle intersect within the circle, prove that the segments of one chord are equal to corresponding segments of the other chord.

If two equal chords of a circle intersect within the circle, prove that the line joining the point of intersection to the centre makes equal angles with the chord.

Equal chords of a circle subtend equal angles at the centre.

If two chords of a circle bisect one another they must be diameters.

If the angles subtended by the chords of a circle at the centre of the circle are equal, then the chords are equal.

If a diameter of a cirlce bisects each of the chords of the circle, prove that the chordds are parallel.

Prove that the right-bisector of a chord of a circle bisects the corresponding minor arc of the circle.

If two circles intersect at two points, prove that their centres lie on the perpendicular bisector of the common chord.