Question

prove that line segment joining the point contact of two parallel tangent to circle is a diameter

Answer 1

Consider AB and CD are two parallel tangents to the circle.  
Consider P and Q be the point of contact and POQ be a line segment.
Construction: Join OP and OQ where O is the centre of a circle.
Proof:  OQ ⊥CD and OP ⊥ AB.
Since AB || CD, OP || OQ.
As OP and OQ pass through O, 
Hence,  POQ is a straight line which passes through the centre of a circle.

Answer 2

$\textbf{Answer is in Attachment !}$