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

Angle in semi-circle is a right angle.

⇒ ∠APB = 90°

Triangle APB is a right triangle with hypotenuse AB. Using Pythagoras theorem,

⇒ AB² = PA² + PB²

⇒ AB² = 10² + 24²

⇒ AB² = 100 + 576

⇒ AB² = 676

⇒ AB = $\sqrt{676}$

⇒ AB = 26 cm

Radius is half of the diameter.

⇒ x = $\dfrac{AB}{2}$

⇒ x = $\dfrac{1}{2} \times 26$ = 13 cm.

Hence, the value of x = 13 cm.