Q10 of 31 Page 234

The points of contact of the tangents from an exterior point P to the circle with centre 0 are A and B. If m∠OPB = 30, then m∠ AOB = ……

In right angled ΔOBP,


Given ∠OBP = 30°



⇒ ∠BOP + ∠OPB + ∠B = 180°


⇒ ∠BOP + 30° + 90° = 180°


⇒ ∠BOP = 180° – 120° = 60°


∴ ∠BOP = 60°


Now, ∠AOB = 2 ∠BOP


= 2 (60°)


= 120°


∴ ∠AOB = 120°

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