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Given: AC and BD are chords of a circle which bisect each other.
To prove: AC and BD are diameters.
Construction : Join AB,BC,CD,DA.
Proof :
In
ABD and 
CDO,
AO = OC (Given )
BO = DO (Given )
So,
ABD
CDO (By SAS)
So, AB || DC ..............1
Also AD || BC ...............2
From 1 and 2,
From 3 and 4,
BD is a diameter of the circle.
Similarly, AC is a diameter.