Question

If tangents are drawn from the end points of $2$ radii that are inclined at an angle ${125}^{\circ }$, what is the angle between the tangents?

• A. ${55}^{\circ }$
• B. ${110}^{\circ }$
• C. ${125}^{\circ }$
• D. ${90}^{\circ }$

Answer 1

The correct option is A ${55}^{\circ }$

Clearly from the figure, by joining radii to both the point of contact, we get quadrilateral & the sum of opposite anlges of a quadrilateral is $180°$

Since, ${180}^{\circ }-\theta ={125}^{\circ }$

$\therefore \theta =(180-125{)}^{\circ }={55}^{\circ }$