1. **Stating the problem:** We have a circle with points A, B, D, and a chord AD. Given that segment AB = 3 cm, BD = X, and X = P, we want to understand the relationships between these segments. 2. **Relevant formula:** In circle geometry, if B lies on the chord AD, then the length of AD is the sum of AB and BD, i.e., $$AD = AB + BD$$. 3. **Substitute known values:** Given $$AB = 3\text{ cm}$$ and $$BD = X = P$$, we have $$AD = 3 + P$$. 4. **Interpretation:** The length of chord AD depends on the value of P, which equals BD. 5. **Summary:** The chord length $$AD$$ is $$3 + P$$ cm, where $$P$$ is the length of segment BD. This completes the solution for the given information.