Let PA and PB are the two tangents to the circle with center O

Given, radius of the circle is √3 cm.

We know that two tangents drawn to a circle from an external point are equally inclined to the segment joining the center to the point.

So, ∠APO = ∠BPO = ∠APB/2 = 60/2 = 30

Again, OA is perpendicular to AP and OB is perpendicular to BP.

Now, in triangle OAP,

tan 30 = OA/PA

=> 1/√3 = √3/PA

=> PA = √3*√3

=> PA = 3 cm

So, PA = PB = 3 cm.

Since, the lengths of the tangents drawn from an external point to the circle are equal,

So, the length of the tangents are 3 cm.