1. **Stating the problem:** Given a circle with chord AB = 7 cm, and segments BE = 5 cm, DE = 6 cm, find the length of CD. 2. **Relevant formula:** By the Power of a Point theorem, for point E outside the circle, $$EB \times EA = ED \times EC$$ where EA and EC are segments from E to points A and C on the circle. 3. **Given values:** $$EB = 5, DE = 6, AB = 7$$ Assuming points A, B, C, D lie on the circle such that AB and CD are chords. 4. **Using the given equation:** From the problem, it is given: $$EB \times AB = DE \times (x + 6)$$ where $x = CD$. 5. **Substitute values:** $$5 \times 7 = 6 \times (x + 6)$$ $$35 = 6x + 36$$ 6. **Solve for $x$:** $$6x = 35 - 36$$ $$6x = -1$$ $$x = -\frac{1}{6}$$ Since length cannot be negative, re-examine the problem or the given data. 7. **Alternative approach:** If the problem intended $EB \times AB = DE \times CD$, then: $$5 \times 7 = 6 \times x$$ $$35 = 6x$$ $$x = \frac{35}{6} \approx 5.83$$ Among the options (a)6, (b)5, (c)4, (d)3, the closest is 6. **Final answer:** $$\boxed{6}$$ cm --- **For the second question:** Given AB = 5 cm, find BE. Since the problem does not provide enough data to solve for BE, and BE is given as 5 cm in the first figure, the answer is: $$\boxed{5}$$ cm