Question

13. In the given figure, tangents AC and AB are drawn to a circle from a point A such thatBAC30. A chord BD is drawn parallel to the tangent AC. Find DBC.

Answer 1

∠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°)
⇒∠RQS=1/2∠SOR
(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)
⇒∠ROS=1/2*60°
⇒30°
∴30° IS THE ANSWER

Answer 2

this is the correct answer of this question