CBSE Class 10CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for In the Given Figure, Pa and Pb Are Two Tangents to the Circle with Centre O. If ∠Apb = 60° Then Find the Measure of ∠Oab. - CBSE Class 10 - Mathematics

Login
Create free account


      Forgot password?

Question

In the given figure, PA and PB are two tangents to the 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 perpendicular 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 isosceles triangle AOB
∠AOB  + ∠OAB + ∠OBA = 180°                [Angle sum property of a triangle]
⇒ 120° +  2 ∠OAB =180°               [∵ ∠OAB = ∠OBA]
⇒  ∠OAB = 30°

  Is there an error in this question or solution?

Video TutorialsVIEW ALL [1]

Solution In the Given Figure, Pa and Pb Are Two Tangents to the Circle with Centre O. If ∠Apb = 60° Then Find the Measure of ∠Oab. Concept: Circles Examples and Solutions.
S
View in app×