Question

Prove that the line segment joining the points of contant of two parallel tangents of a circle passes through its centre.

Answer 1

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 ABllCD, OPllOQ.

As OP and OQ pass through O, 

Hence,  POQ is a straight  line which passes through the centre of a circle.