Question

If the angle between two radii of a circle is ${100}^{\circ }$, the angle between the tangents at the ends of those radii is :

• A. ${50}^{\circ }$
• B. ${60}^{\circ }$
• C. ${80}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is C ${80}^{\circ }$

From the figure, it is evident that $\angle AOB={100}^{\circ }$.

Now, $\angle OAP={90}^{\circ }$ and $\angle OBP={90}^{\circ }$ (radii is perpendicular to tangent at point of contact)

Also, sum of interior angles of a quadrilateral is ${360}^{\circ }$ and hence,

$\angle APB={360}^{\circ }-\angle OAP-\angle OBP-\angle AOB={80}^{\circ }$

This is the required angle between the tangents.