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The angle between two radii of a circle is 60°. The angle between their corresponding tangents is :

  1. 60°

  2. 90°

  3. 120°

  4. 150°

Constructions

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Answer

From figure,

The angle between two radii of a circle is 60°. The angle between their corresponding tangents is : Constructions, Concise Mathematics Solutions ICSE Class 10.

∠OAP = ∠OBP = 90° [The radius and tangent of a circle at a point of contact is always perpendicular to each other.]

In quadrilateral OABP,

By angle sum property of quadrilateral,

⇒ ∠OAP + ∠OBP + ∠AOB + ∠APB = 360°

⇒ 90° + 90° + 60° + ∠APB = 360°

⇒ 240° + ∠APB = 360°

⇒ ∠APB = 360° - 240° = 120°.

Hence, Option 3 is the correct option.

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