110EXEMPLAR PROBLEMS
In Fig. 9.18, tangents PQ and PR are drawn to a circle such that
∠RPQ =30°. A chord RS is drawn parallel to the tangent PQ. Find the
∠RQS.

∠RPQ = 30°

RS is parallel to PQ, thus PR is transversal.

∴ ∠SRP + ∠QPR = 180°

⇒ ∠SRP = 180° – ∠QPR = 180° – 30° = 150°

∠ORP = 90° (OR ⊥ PR)

⇒ ∠SRO = ∠SRP – ∠ORP

⇒∠SRO = 150° – 90° = 60°

∴ ∠RSO = ∠SRO = 60° (OS = OR = Radius)

∠SOR = 60°  (∠RSO + ∠SRO + ∠SOR = 180°)

[Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle]

 = 30°

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