In figure given below, O is the centre of the circle, use the given information to find the value of x:

At the point of contact, the angle between tangent and the radius is always 90°.

⇒ ∠OAB = 90°

Triangle OAB is a right triangle with hypotenuse OB. Using Pythagoras theorem,

⇒ OB² = OA² + AB²

⇒ 10² = 8² + AB²

⇒ 100 = 64 + AB²

⇒ AB² = 100 - 64

⇒ AB² = 36

⇒ AB = $\sqrt{36}$

⇒ AB = 6 cm

We know that,

Tangents from an exterior point to a circle are equal in length.

⇒ BC = BA

⇒ x = 6 cm.

Hence, the value of x = 6 cm.