Q4 of 47 Page 1

In Fig. 1, PA and PB are tangents to the circle with center O such that . Write the measure of .


As we know that the angle opposite to equal sides are equal.


∴ ∠1 = ∠2 ……(1)


Sum of all the angles of a triangle is 180°.


In Δ PAB,


∠1 + ∠2 + ∠APB = 180°


⇒ ∠1 + ∠2 + 50° = 180° (given ∠APB = 50°)


⇒ ∠1 + ∠2 = 130°


⇒ ∠1 + ∠1 = 130° (From equation 1)


⇒ 2∠1 = 130°


⇒ ∠1 = 65° ….(2)


We know that the angle between the tangent and radius is 90° .


∴ ∠1 + ∠OAB = 90°


⇒ 65° + ∠OAB = 90° (From equation 2)


⇒ ∠OAB = 25°


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