Given:

OA = 6 cm

OB = 8 cm

Property: The tangent at a point on a circle is at right angles to the radius obtained by joining center and the point of tangency.

By above property, ∆AOB is right-angled at ∠OAB (i.e., ∠OAB = 90°).

Therefore by Pythagoras theorem,

OA² + AB² = OB²

⇒ AB² = OB² – OA²

⇒ AB² = 8² – 6²

⇒ AB² = 64– 36

⇒ AB² = 28

⇒ AB= √28

⇒ AB= 2√7

Hence, length of tangent is 2√7 cm.