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Two chords A B\ a n d\ C D of a circle ...

Two chords `A B\ a n d\ C D` of a circle are parallel and a line `l` is the perpendicular bisector of `A Bdot` Show that `l` bisects `C D`

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We know that the perpendicular bisector of any chord of a circle always passes through its centre.
Since l is the perpendicular bisector of AB, l passes through the centre O of the circle.

Now, `l _|_` AB and `AB ||CD implies l_|_ CD`
Thus, `l _|_ CD` and passes through the centre of the circle.
But, the perpendicular from the centre ofa circle to a chords bisects the chord.
`:. ` l must bisect the chord CD.
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