Question

prove that, if a diameter of a circle bisects two chords of a circle then those two chords are parallel to each other​

Answer 1

There are two chords AB and CD , which are bisected by the diameter

Since, ON bisects CD, therefore ON is perpendicular  to CD

Similarly, OM is perpendicular to AB

To prove that the two chords are parallel we need to show their alternative interior angles are equal

Since, For chord AB and CD , MN act as a transversal and also

Angle AMN = Angle MND ( both are 90 degree)

Hence we can say both Chord AB and CD are parallel to each other.

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