**Question:**

To draw a pair f tangents to a circle which are inclined to each other at an angle of 100°, It is required to draw tangents at end points of those two radii of the circle, the angle between which should be:

(a) 100°

(b) 50°

(c) 80°

(d) 200°

**Solution:**

Given a pair of tangents to a circle inclined to each other at angle of 100°

We have to find the angle between two radii of circle joining the end points of tangents that is we have to find in below figure.

Let *O *be the center of the given circle

Let *AB *and *AC *be the two tangents to the given circle drawn from point *A*

Therefore ∠*BAC* = 100°

Now *OB *and *OC *represent the radii of the circle

Therefore

[Since Radius of a circle is perpendicular to tangent]

We know that sum of angles of a quadrilateral = 360°

Therefore in Quadrilateral *OBAC*

$\angle B A C+\angle A C O+\angle C O B+\angle O B A=360^{\circ}$

$100^{\circ}+90^{\circ}+\angle C O B+90^{\circ}=360^{\circ}$

$\angle C O B=360^{\circ}-280^{\circ}$

$\angle C O B=80^{\circ}$

Hence Option (*c*) is correct.