If a chord is at a distance of 8 cm from the centre of the circle of radius 17 cm, then the length of the chord will be :

1. 15 cm

2. 20 cm

3. 30 cm

4. 45 cm

Let the chord be AB and the perpendicular from the center O meet the chord at M.

In the right-angled triangle △OMA:

Using the Pythagorean theorem:

OA² = AM² + OM²

17² = AM² + 8²

289 = AM² + 64

AM² = 289 - 64

AM² = 225

AM = $\sqrt{225}$ = 15 cm

Since the perpendicular from the center bisects the chord.

Length of chord = 2 × AM = 30 cm.

Hence, option 3 is the correct option.