Given:

Radius of the circle = r = AO = 5 cm

Length of chord AB = 8 cm

Since the line drawn through the center of a circle to bisect a chord is perpendicular to the chord, therefore AOC is a right angled triangle with C as the bisector of AB.

∴ AC = 1/2(AB) = 8/2 = 4 cm

In right angled triangle AOC, by Pythagoras theorem, we have:

(AO)² = (OC)² + (AC)²

⇒ (5)² = (OC)² + (4)²

⇒ (OC)² = (5)² - (4)²

⇒ (OC)² = 25 – 16

⇒ (OC)² = 9

Take square root on both sides:

⇒ (OC) = 3

∴ The distance of AC from the center of the circle is 3 cm.

Now, OD is the radius of the circle, ∴ OD = 5 cm

CD = OD – OC

CD = 5 – 3

CD = 2

∴ CD = 2 cm