To solve the problem of finding the length of the chord, we use the relationship between the radius of the circle, the distance from the center to the chord, and the chord length.

Step 1: Key Observations

A perpendicular from the center of the circle to a chord bisects the chord. This forms a right triangle with:

• Hypotenuse = radius of the circle ((r = 5) cm),
• One leg = distance from center to chord ((d = 3) cm),
• The other leg = half the length of the chord ((l)).

Step 2: Apply Pythagoras Theorem

[r^2 = d^2 + l^2]

Substitute the values:
[5^2 = 3^2 + l^2]
[25 = 9 + l^2]
[l^2 = 25 - 9 = 16]
[l = 4] cm

Step 3: Full Chord Length

Since (l) is half the chord length:
Total chord length = (2l = 2×4 = 8) cm

Answer: (\boxed{8}) cm.

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