CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠APB = 60 then ∠OAB is [CBSE 2011]
(a) 15
(b) 30
(c) 60
(d) 90

Open in App
Solution

Construction: Join OB


We know that the radius and tangent are perperpendular at their point of contact
∵∠OBP = ∠OAP = 90
Now, In quadrilateral AOBP
∠AOB + ∠OBP + ∠APB + ∠OAP = 360 [Angle sum property of a quadrilateral]
⇒ ∠AOB + 90 + 60+ 90 = 360
⇒ 240 + ∠AOB = 360
⇒ ∠AOB = 120
Now, In isoceles triangle AOB
∠AOB + ∠OAB + ∠OBA = 180 [Angle sum property of a triangle]
⇒ 120 + 2∠OAB = 180 [∵∠OAB = ∠OBA ]
⇒ ∠OAB = 30
Hence, the correct answer is option (b).

flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Intersection between Tangent and Secant
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon