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∘
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2
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.
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3
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
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