prove that the line joining the midpoint of two parallel chords of a circle passes through the centre of a circle
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Draw AB and CD,
the parallel chords of a circle such that M and N are the midpoints of the chords respectively.
The perpendicular bisector of the chord passes through the centre.
,
So
ON ⊥ CD. and OM ⊥ AB.
But AB || CD
Therefore,
NOM is a straight line.
Hence the line joining the midpoints of two chords of a circle parallel to each other passes through the centre of the circle.
the parallel chords of a circle such that M and N are the midpoints of the chords respectively.
The perpendicular bisector of the chord passes through the centre.
,
So
ON ⊥ CD. and OM ⊥ AB.
But AB || CD
Therefore,
NOM is a straight line.
Hence the line joining the midpoints of two chords of a circle parallel to each other passes through the centre of the circle.
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