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 end points of those two radii of the circle, the angle between them should be ______.

Question

KollegeApply · Accepted Answer

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 end points of those two radii of the circle, the angle between them should be $120^\circ$. Explanation: 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 radii tangents (at which tangents are drawn) and the centre of the circle is a quadrilateral. From figure it is quadrilateral, $\angle$POQ + $\angle$PRQ = $180^\circ$ ...[$\therefore$ Sum of opposite angles are $180^\circ$] $\therefore$ $60^\circ$ + $\theta$ = $180^\circ$ $\theta$ = $120^\circ$ Hence, the required angle between them is $120^\circ$. [Solution diagram: 258670_solution_1.png]

AChoose Your Answer