Question

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

Answer 1

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To Prove:- AOB is a straight line passing through O.

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

Join AO and OB. Draw OC II PQ.

Now PA ll CO

⇒ ∠PAO + ∠COA = 180°

(sum of angles at the same side if transversal is 180°)

⇒ 90° + ∠COA = 180°

(angle between a tangent and radius = 90°)

⇒ ∠COA = 90°

Similarly,

⇒ ∠COB = 90°

∠COA +∠COB = 90° + 90° = 180°

Hence, AOB is a straight line passing through O.

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