NumericalModerate2 marks
7(c)
In the given figure TP and TQ are two tangents to the circle with centre O, touching at A and C respectively. If ∠BCQ = 55° and ∠BAP = 60°, find :
∠OBA and ∠OBC
Topic: Tangents / intersecting chords
Previous-year question practice database
Answer
Exam answer
At A, OA is a radius and AP is tangent.
Therefore:
∠OAP = 90°
Given:
∠BAP = 60°
Hence:
∠OAB = 90° − 60° = 30°
OA = OB because both are radii.
Therefore in ΔOAB:
∠OBA = 30°
Similarly, at C:
OC ⟂ CQ
∠OCQ = 90°
Given:
∠BCQ = 55°
Therefore:
∠OCB = 90° − 55° = 35°
OB = OC because both are radii.
Therefore in ΔOBC:
∠OBC = 35°
Answer:
∠OBA = 30° ∠OBC = 35°.
Explanation
A radius is perpendicular to the tangent at the point of contact. The equal radii then make triangles OAB and OBC isosceles, so their respective base angles are equal.