Question

If two tangents drawn on a circle of radius 3 cm are inclined to each other at an angle of \( 60^\circ \), then the length of each tangent is

• A. \( 2\sqrt{3} \, \text{cm} \)
• B. \( \frac{3\sqrt{3}}{2} \, \text{cm} \)
• C. \( 3\sqrt{3} \, \text{cm} \)
• D. 4 cm

Hint:

Always confirm the geometric relationships and trigonometric formulas relevant to the problem at hand to ensure accuracy.

Answer 1

The Correct Option is C

Step 1: The length \( L \) of each tangent from a point external to a circle can be found using the formula: \[ L = r \cdot \tan \left(\frac{\theta}{2}\right) \] Step 2: Substituting \( r = 3 \, \text{cm} \) and \( \theta = 60^\circ \): \[ L = 3 \cdot \tan(30^\circ) = 3 \cdot \frac{1}{\sqrt{3}} = \sqrt{3} \times 3 = 3\sqrt{3} \, \text{cm} \] Thus, the correct answer is \( \boxed{3\sqrt{3} \, \text{cm}} \).