Q. 11

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

Answer :


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.


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