Question

Prove that the line segment joining the points if contact of two circle of two parallel tagents a circle passes through its centre?????

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.