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If a line segment joining the mid points of 2 chords of a circle passes throgh the centre of the circle , prove that 2 chords are parallel.

Posted by Shashant Ahuja 8 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Shweta Gulati 8 years, 10 months ago

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.

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CBSE > Class 09 > Mathematics