Prove that the line segment joining the mid-points of two parallel chords of a circle passes through the centre of the circle.

Let AB and CD be the two parallel chords of a circle such that M and N are the mid-points of AB and CD respectively.

Since the perpendicular bisector of the chord passes through the centre,

⇒ ON ⊥ CD and OM ⊥ AB

Since AB || CD, NOM is a straight line.

Hence the line joining the midpoints of two parallel chords of a circle passes through the centre of the circle.