1. **Stating the problem:** We are given two chords intersecting inside a circle with lengths AE = 5 cm, CE = 8 cm, DE = 10 cm, and BE = (x + 1) cm. We need to find the value of $x$. 2. **Formula used:** When two chords intersect inside a circle, the products of the segments of each chord are equal. This is called the Intersecting Chords Theorem: $$CE \times ED = AE \times EB$$ 3. **Substitute the known values:** $$8 \times 10 = 5 \times (x + 1)$$ 4. **Calculate the left side:** $$80 = 5(x + 1)$$ 5. **Divide both sides by 5 to isolate $(x + 1)$:** $$\frac{80}{5} = x + 1$$ $$16 = x + 1$$ 6. **Solve for $x$:** $$x = 16 - 1$$ $$x = 15$$ 7. **Answer:** The value of $x$ is 15 cm. This corresponds to option (d) 15.