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If a diameter of a circle bisects eac...

If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel.

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Let AB and CD be two chords ofa circle C(O,r).
Let PQ be a diameter , bisecting chords AB and CD at L and M respectively.
Since PQ is a diameter of the circle, it passes through the centre O.
Now L is the midpoint of AB.
We know that the joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.
`:. OL _|_ AB `
`implies /_ALO =90^(@)`
Similarly , `/_ DMO =90^(@)`
`:. /_ALO = /_ DMO `.
But , these are alternate angles.
`:. AB || CD`.
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