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.

 

 

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