If pa and pb are two tangents drawn to a circle with centre o from p such that pba=50

In figure, if PA and PB are tangents to the circle with centre O such that ∠ APB =50∘, then ∠ OAB is equal to:A. 30∘B. 25∘C. 40∘D. 50∘

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

In the given figure, PA and PB are two tangents to the circle with centre O. If ∠ APB = 50o then what is the measure of ∠ OAB.

Open in App

From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB = 50°, then find ∠AOB.

It is given that PA and PB are tangents to the given circle.

∴∠PAO=90°      (Radius is perpendicular to the tangent at the point of contact.)

Now

∠PAB=50°          (Given)

∴∠OAB=∠PAO−∠PAB=90°−50°=40°

In ∆OAB,

OB = OA    (Radii of the circle)

∴∠OAB=∠OBA=40°           (Angles opposite to equal sides are equal.)

Now

∠AOB+∠OAB+∠OBA=180°       (Angle sum property)

⇒∠AOB=180°−40°−40°=100°

Concept: Number of Tangents from a Point on a Circle

  Is there an error in this question or solution?