Question

Two tangents making an angle of 120° with each other are drawn to a circle of radius 6 cm, then the length of each tangent is equal to

(a) $\sqrt{3}cm$

(b) 6 $\sqrt{3}cm$

(c) $\sqrt{2}cm$

(d) 2 $\sqrt{3}cm$

Answer 1

We are given two tangents to a circle making an angle of 120° with each other. The radius of circle is 6 cm

We have to find the length of each tangent.

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

Now OB and OC represent the radii of the circle

Therefore

[Since Radius of a circle is perpendicular to tangent]

Therefore by SSS rule

Hence [Corresponding angles of congruent triangles]

In right

Hence option (d) is correct.