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Question

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

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Solution

Given: PAQ and RBS be two parallel tangents to a circle with centre O.
To Prove:
AOB is a straight line(joining two tangents) passing through center O..
Proof
Join
OAandOB. Draw OCPQ.
Now, PAparallelCO
PAO+COA=180
[Sum of co-interior angle is 180]
90+COA=180[PAO=90]
COA=90
Similarly, COB=90
COA+COB=90+90=180
Hence, AOB is a straight line passing through O

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