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°.