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To solve this problem, let's analyze the geometry in the circle and apply appropriate calculations.

### Given Information:
- \( OC = 20 \, \text{cm} \)
- \( CE = 8 \, \text{cm} \)
- We need to find the length of the chord \( AB \).

### Solution Approach:
1. **Determine the Radius \( r \):**
   Since \( O \) is the center of the circle and \( OC \) is a radius, we have:
   \[
   r = OC = 20 \, \text{cm}
   \]

2. **Identify Triangle \( OEC \):**
   Triangle \( OEC \) is a right triangle with:
   - \( OE \) as one leg,
   - \( CE = 8 \, \text{cm} \) as the other leg,
   - \( OC = 20 \, \text{cm} \) as the hypotenuse.

3. **Calculate \( OE \) Using the Pythagorean Theorem:**
   \[
   OE^2 + CE^2 = OC^2
   \]
   Substituting the values:
   \[
   OE^2 + 8^2 = 20^2
   \]
   \[
   OE^2 + 64 = 400
   \]
   \[
   OE^2 = 336
   \]
   \[
   OE = \sqrt{336} = 4\sqrt{21} \approx 18.33 \, \text{cm}
   \]

4. **Determine \( AB \):**
   Since \( AB \) is a chord perpendicular to \( OE \) at \( E \), and \( E \) is the midpoint of \( AB \), we can calculate \( AB \) using the formula for a chord:
   \[
   AB = 2 \sqrt{OC^2 - OE^2}
   \]
   Substituting the values:
   \[
   AB = 2 \sqrt{20^2 - (4\sqrt{21})^2}
   \]
   \[
   AB = 2 \sqrt{400 - 336} = 2 \sqrt{64} = 2 \times 8 = 16 \, \text{cm}
   \]

### Answer:
The length of chord \( AB \) is \( \boxed{16 \, \text{cm}} \), which corresponds to option **A. 16 cm**.

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Do you want more details or have any questions?

Here are five related questions to explore further:
1. How do we calculate the radius of a circle if given only a chord and a perpendicular distance from the center?
2. What other methods can we use to find the length of a chord in a circle?
3. How would the length of \( AB \) change if the radius of the circle was different?
4. What is the significance of the Pythagorean theorem in solving circle problems?
5. Can this problem be solved using trigonometric methods?

**Tip:** For problems involving chords in a circle, drawing perpendiculars from the center can often simplify calculations significantly.

Pada gambar di bawah, panjang OC = 20 cm dan CE = 8 cm. Panjang tali busur AB adalah...

Learn how to calculate the length of a chord in a circle given the radius (OC = 20 cm) and the distance from the center to the chord (CE = 8 cm). This problem uses geometry, the Pythagorean theorem, and the chord length formula. Suitable for students in Grades 10-12.

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