Can you please give me the proof for this...?

Question

A diameter AB of a circle bisects a chord PQ. If AB is parallel to PQ, prove that the chord PQ is also a diameter to the circle.

Answer 1

I think you mean
"a diameter AB of a circle bisects a chord PQ. If AB is NOT PERPENDICULAR to PQ, prove that the chord PQ is also a diameter to the circle".

In fact, the only case in which a diameter bisecting a chord can be not perpendicular to that cord is when the cord is a diameter too.

To prove that, let R be the intersection point of AB and PQ. One has to prove that R=O, the center of the circle. Then PR=RQ and
ARP=BRQ
APQ=ABQ
as angles. Then the triangles APR and BRQ
are equals. It follows
AR=RB=radius, so R=O
Q.E.D.

Answer 2

I believe there is a contradiction here. AB cannot bisect PQ and also be parallel to it.

Answer 3

if AB is parallel to PQ it cannot bisect it