Question

If tangents are drawn from the endpoints of two radii that are inclined at an angle ${105}^{\circ }$, what is the angle between the tangents?

• A. $5^{\circ }$
• B. ${35}^{\circ }$
• C. ${75}^{\circ }$
• D. None of these

Answer 1

Answer: (C)

${75}^{\circ }$

Tangent is perpendicular to radius at the point of contact.

Therefore $\angle OQP=\angle ORP={90}^{\circ }$

Sum of all the four angles of a quadrilateral is ${360}^{\circ }$

So in quadrilateral QORP

$\angle PQO+\angle QOR+\angle ORP+\angle RPQ={360}^{\circ }$

${90}^{\circ }+{105}^{\circ }+{90}^{\circ }+\angle RPQ={360}^{\circ }$ [Given $\angle QOR={105}^{\circ }$]

$\angle RPQ={360}^{\circ }-{285}^{\circ }$

$\angle RPQ={75}^{\circ }$

Threfore option c is the answer.