Problem:
If the radii of two concentric circles are 15 and 17, find the length of each chord of one circle that is tangent to the other.

Solution:

Given:
- Radii of two concentric circles: 15 and 17

Approach:
To find the length of each chord of one circle that is tangent to the other, we can use the following steps:

1. Identify the two concentric circles and label them:
- Circle A with radius 15
- Circle B with radius 17

2. Draw a chord on Circle A that is tangent to Circle B.
- Let's call this chord AB.

3. Label the points of tangency between the chord AB and Circle B as P and Q.

4. Draw radii from the center O of the concentric circles to the points of tangency P and Q.
- Label these radii as OP and OQ.

5. Since OP and OQ are radii of Circle B, their lengths are equal to the radius of Circle B, which is 17 units.

6. Observe that the chord AB is perpendicular to the radius OP.
- This is because, at the point of tangency, the line drawn from the center of the circle to the point of tangency is always perpendicular to the tangent line.

7. Use the Pythagorean theorem to find the length of the chord AB.
- The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.

8. In the right triangle OPB, OP is the hypotenuse, and PB is the other side.
- The length of OP is 17 units (as mentioned in step 5).

9. Let's assume that the length of the chord AB is x units.
- The length of PB can be calculated by subtracting the length of AB from the radius of Circle A (15 - x).

10. Apply the Pythagorean theorem:
- (15 - x)^2 + PB^2 = OP^2
- (15 - x)^2 + PB^2 = 17^2
- Simplify and solve this equation to find the value of x, which represents the length of the chord AB.

Answer:
Based on the above steps, we can determine the length of each chord of one circle that is tangent to the other by solving the equation obtained in step 10.