Answer :

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

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