Question

Question 6
To draw a pair of tangents to a circle which are inclined to each other at an angle of ${60}^{\circ }$, it is required to draw tangents at endpoints of those two radii of the circle, the angle between them should be
(A) ${135}^{\circ }$
(B) ${90}^{\circ }$
(C) ${60}^{\circ }$
(D) ${120}^{\circ }$

Answer 1

The angle between them should be ${120}^{\circ }$ because in that case the figure formed by the intersection point of pair of tangent, the two end points of those two two radii (at which tangents are drawn) and the centre of the circle is a quadrilateral.

From figure it is quadrilateral.
$\angle POQ+\angle PRQ={180}^{\circ }$ [sum of opposite angles are 180]
${60}^{\circ }+\theta ={180}^{\circ }$
$\theta ={120}^{\circ }$
Hence, the required angle between them is ${120}^{\circ }$