Question

If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm then the length of each tangent is equal to ______

Options

• 3 cm

• `(3sqrt(3))/2 ` cm

• `3sqrt(3)` cm

• 6 cm

Answer 1

If two tangents inclined at an angle of 60° are drawn to a circle of radius 3 cm then the length of each tangent is equal to `underlinebb(3sqrt(3)  cm)`.

Explanation:

Let P be an external point from which pair of tangents are drawn as shown in the figure given below:

Join OA and OP

Also, OP is a bisector line of ∠APC.

∠APO = ∠CPO = 30°

OA ⊥ AP

Therefore, in triangle OAP

tan 30° = `"OA"/"AP"`

`1/sqrt3 = 3/"AP"`

AP = `3sqrt3` cm