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Question

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

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Solution

To prove: AOB is a straight line passing through O.

Let PAQ and RBS be two parallel tangents to a circle with centre O.

Join OA and OB. Draw OC || PQ.

Now, PA || CO

PAO+COA=180o [Sum of the angle on the same side of a transversal is 180o]

90o+COA=180o [PAQ=angle between a tangent and radius=90o]

COA=90o

Similarly, COB=90o

COA+COB=90o+90o=180o

Hence, AOB is a straight line passing through O.

1031575_1009678_ans_a9b35fc4345d43f18cdc33feb339b2cc.png

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