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Question
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be ______.
Options
135°
90°
60°
120°
Solution
To draw a pair of tangents to a circle which are inclined to each other at an angle of 60°, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be 120°.
Explanation:
The angle between them should be 120° because in that case the figure formed by the intersection point of pair of tangent, the two end points of those two radii tangents (at which tangents are drawn) and the centre of the circle is a quadrilateral.
From figure it is quadrilateral,
∠POQ + ∠PRQ = 180° ...[∴ Sum of opposite angles are 180°]
∴ 60° + θ = 180°
θ = 120°
Hence, the required angle between them is 120°.
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