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 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°.
