Question

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Hello

My question :

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

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Answer 1

Hope this will help u... :-)

Answer 2

Sol:

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.