Let C be a circle with center O and P be an external point to C. Let PA and PB be two tangents to C with A and B being the points of tangency, respectively. If PA and PB are inclined to each other at an angle of 60°, then find∠POA.
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 60°.
⇒ ∠OPA = 60/2 = 30°
⇒ ∠OAP = 90° [tangent on the circle]
Now, in ΔOAP
⇒ ∠OAP + ∠OPA + ∠POA = 180°
⇒ 90° + 30° + ∠POA = 180°
⇒ ∠POA = 180° - 120°
⇒ ∠POA = 60°