Question

Prove that the segment joining the points of contact of two parallel tangents passes through center

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

Refer to the above attachment

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