Question

If two tangents inclined at an angle of ${60}^{\circ }$, are drawn to a circle of radius 3 cm, then length of each tangent (in cm) is equal to :

• A. 3
• B. 6
• C. $\frac{3}{2}\sqrt{3}$
• D. $3\sqrt{3}$

Answer 1

The correct option is D $3\sqrt{3}$

The tangent to any circle is perpendicular to the radius of the circle at point of contact.

Let two Tangents originate from point A and touch the circle with centre O at point B & C

Now ABO is a right triangle with angle A as 30° and angle B as 90°

Given OB = 3 = Radius of circle.

Now $\frac{OB}{AB}$ = tan 30°

=> $AB=\frac{OB}{tan30°}$

=$\frac{3}{\left(1/\sqrt{3}\right)}=3\sqrt{3}$

Similarly, it can be shown that $AC=3\sqrt{3}$

option D will the answer.