Question

Prove prove that the line segment joining the points of contact of two parallel tangents passes through the centre??

Answer 1

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given :- Consider AB and CD are two || tangents of a circle .

Construction :- Join OP and OQ where O is the center of a circle .

Proof :- OQ perpendicular CD , OP perpendicular AB

Since AB || CD , OP || OQ

sense POQ is the straight line which passes through the center of a circle .

Hope this will helps u...

Answer 2

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 ABCD, OPOQ.

As OP and OQ pass through O, 

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


$hope \: helps$


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