Q6 of 52 Page 10

In fig. 2, PA and PB are tangents to the circle with center O. If∠ APB=60°, then calculate∠ OAB. (CBSE 2012)

 

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°.


∠1 + ∠2 + ∠APB=180°


∠1 + ∠2 + 60° =180° (given ∠APB=100° )


∠1 + ∠2=120°


∠1 + ∠1=120° (From equation 1)


2∠1=120°


∠1=60° …………….(2)


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


∴ ∠1 + ∠OAB=90°


60° + ∠BAT=90° (From equation 2)


∠BAT=30°

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