Line joining the midpoints of two chords of a circle passes through its Centre .prove that the chords are parallel

We have-

Let AB and CD be the parallel chords of a circle such that M and N are the mid - point of the respective chords.

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

So,

ON is perpendicular to CD.

OM is perpendicular to 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 center of circle.