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°