By an external point P, two tangents are drawn to a circle, touching the circle at points A and B. The chord of contact AB subtends an angle θ at the center of the circle O. What is the ∠APB between the tangents in terms of θ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. .
Quadrilateral OAPB: ∠OAP = ∠OBP = 90°
∠AOB = θ
Sum of angles in a quadrilateral = 360°
⇒ 90° + 90° + θ + ∠APB = 360°
⇒ ∠APB = 180° – θ