From an external point P, tangents PA and PB are drawn to a circle with centre O. If ∠PAB= 55°, find ∠AOB.

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  1. 110°
  2. 100°
  3. 35°
  4. 125°

Answer (Detailed Solution Below)

Option 1 : 110°
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Detailed Solution

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Given:

PA and PB are the tangents to the circle with centre O. 

∠PAB= 55°

Concept:

Tangents drawn from the same external point are equal in length. 

A tangent perpendicular to the radius at the point of tangency.

Calculation:

∵ ∠PAB = 55° 

∴ ∠PBA = 55° (PA = PB) 

In triangle PAB,  

∠APB + ∠PAB + ∠PBA = 180°  (Angle Sum Property)

⇒ ∠P + 55° + 55° = 180° 

⇒ ∠P = 70° 

Also, ∠AOB + ∠APB = 180°   (Sum of all the angles of a quadrilateral is 360° & ∠P = 70° ∠B = 90°)

⇒ ∠AOB = 180° - 70° = 110

∴ The measure of ∠AOB = 110° 

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