In the given figure, PA and PB are two tangents to a circle with centre O,

Question:

In the given figure, PA and PB are two tangents to a circle  with centre O, If ∠APB = 60 then find the measure of ∠OAB

 

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 = 1200 
Now, In isoceles triangle AOB
∠AOB + ∠OAB + ∠OBA = 180            [Angle sum property of a triangle]
⇒ 120 +  2∠OAB = 180                          [∵∠OAB = ∠OBA ]
⇒ ∠OAB = 30

 

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now