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Mathematics

In the above figure, if ∠P = 50°, then reflex angle AOB is :

  1. 2 × 50°

  2. 180° - 60°

  3. 230°

  4. none of these

In the above figure, if ∠P = 50°, then reflex angle AOB is : Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

Join OB.

In the above figure, if ∠P = 50°, then reflex angle AOB is : Concise Mathematics Solutions ICSE Class 10.

We know that,

Tangent at any point of a circle and the radius through this point are perpendicular to each other.

∴ ∠OAP = 90° and ∠OBP = 90°

In quadrilateral OAPB,

⇒ ∠OAP + ∠APB + ∠PBO + ∠AOB = 360°

⇒ 90° + 50° + 90° + ∠AOB = 360°

⇒ ∠AOB + 230° = 360°

⇒ ∠AOB = 360° - 230° = 130°.

Reflex ∠AOB = 360° - ∠AOB = 360° - 130° = 230°.

Hence, Option 3 is the correct option.

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