Question

If tangents are drawn from end points of 2 radii inclined at angle ${155}^{\circ }$, what is the angle between the tangents?

• A. ${90}^{\circ }$
• B. ${155}^{\circ }$
• C. ${35}^{\circ }$
• D. ${25}^{\circ }$

Answer 1

Answer: (D)

${25}^{\circ }$

Tangent is perpendicular to radius at the point of contact.

Therefore $\angle OPQ=\angle ORQ={90}^{\circ }$

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

So, $\angle OPQ+\angle PQR+\angle QRO+\angle ROP={360}^{\circ }$

${90}^{\circ }+\angle PQR+{90}^{\circ }+{155}^{\circ }={360}^{\circ }$ [Given $\angle POR={155}^{\circ }$]

$\angle PQR={25}^{\circ }$

Therefore angle between the tangents ${25}^{\circ }$

So, option D is the answer.