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A B\ a n d\ C D are two parallel chor...

`A B\ a n d\ C D` are two parallel chords of a circle whose diameter is `A C` . Prove that `A B=C D`

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In the figure O is centre of the circle.
Draw `OMbotAB` and `ONbotCD`.
In `DeltaOAM` and `Delta OCN`, we have
`because" "{(angleOAM,=,,angle OCN,("alternate angles")),(angleOAM,=,,angleONC,("given"=90^@)),(OA,=,,OC,("radii of same circle")):}`
`thereforeDelta OAMcongDeltaOCN` (AAS congurency
`AM=CN` (c.p.c.t)
`2AM=2CN`
`rArrAB=CD` (because Perpendiculars from centre bisect the chords)
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