To draw a pair of tangents to a circle

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

(a) 135°                     

(b) 90°                       

(c) 60°                        

(d) 120°

Solution:

(d) 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 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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