Mathematics
The angle between two radii of a circle is 60°. The angle between their corresponding tangents is :
60°
90°
120°
150°
Constructions
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Answer
From figure,
∠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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