Given:
- Radius of the circle = 17 cm
- Distance of the chord from the center of the circle = 8 cm

To find:
- Length of the chord

Solution:
Step 1: Draw a diagram

Let's start by drawing a diagram to represent the given information. We have a circle with a radius of 17 cm, and a chord that is at a distance of 8 cm from the center of the circle.

```
O
|\
| \
| \
17 | \ 17
| \
| \
|8 \
|______\
```

Step 2: Connect the chord to the center of the circle

To find the length of the chord, we need to connect the endpoints of the chord to the center of the circle and form a right triangle.

```
O
|\
| \
| \
17 | \ 17
| \
| \
|8 \
|______\
\ x /
\ /
\ /
C
```

Step 3: Use the Pythagorean theorem to find the length of the chord

In the right triangle, we can use the Pythagorean theorem to find the length of the chord. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let the length of the chord be x.

Using the Pythagorean theorem, we have:
(17^2) = (x^2) + (8^2)
289 = x^2 + 64
x^2 = 289 - 64
x^2 = 225
x = √225
x = 15

Step 4: Determine the length of the chord

Therefore, the length of the chord is 15 cm.