Dear Vaibhav
The angle between the tangent and any chord at the point of contact is equal to the angle subtended by the arc on the alternate segmenta of the arc.
Let T P T' be the tangent.
The angle T P A = angle A B D ( through the point of contact P), by reason of above theorem.
Similarly, angle T' P C = angle C D B.
But angle T P A = angle T' P C as they are opposite angle.
Therefore, angle A B D = angle C D B. So the alternate angles are equal, BD being the transversal.
This implies AB || CD.
Regards
Arun (askIITians forum expert)
