Prove that the line segment joining the points of contact of two parallel tangents passes through center of circle .
Let AB and CD are two parallel tangents to the circle. Let 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.