Question

To draw a pair of tangents to a circle which are inclined to each other at an angle of ${35}^{\circ }$, it is required to draw tangents at the end point of those two radii of the circle, the angle between them is:

• A. ${70}^{\circ }$
• B. ${110}^{\circ }$
• C. ${140}^{\circ }$
• D. ${145}^{\circ }$

Answer 1

The correct option is D ${145}^{\circ }$

PA and PB are tangents drawn from an external point P to the circle.

$\angle OAP=\angle OBP={90}^{\circ }$ (Radius is perpendicular to the tangent at point of contact)

In quadrilateral OAPB,

$\angle APB+\angle OAB+\angle AOB+\angle OBP={360}^{\circ }$

${35}^{\circ }+{90}^{\circ }+\angle AOB+{90}^{\circ }={360}^{\circ }$

${215}^{\circ }$ +$\angle AOB$ = ${360}^{\circ }$

$\angle AOB={360}^{\circ }–{280}^{\circ }={145}^{\circ }$

Thus, the angle between the two radii, OA and OB is ${145}^{\circ }$.