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°

Answer 1

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

Hence Option (c) is correct.