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To find the length of \( CE \), we can use the property of the centroid in a triangle.

### Key Information:
1. \( D \) is the centroid of \( \triangle ABC \).
2. The centroid divides each median in the ratio 2:1, meaning \( AD : DG = 2 : 1 \), \( BE : ED = 2 : 1 \), and \( CF : FD = 2 : 1 \).
3. The given length \( ED = 12 \).

### Solution:
Since \( D \) is the centroid, it divides \( BE \) in the ratio 2:1. This implies:
\[
BE = 3 \times ED = 3 \times 12 = 36
\]

Thus, \( BE = 36 \), and therefore \( CE = BE = 36 \).

### Answer:
\[
CE = 36
\]

Would you like further details or have any questions on this topic?

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Here are five additional questions related to this topic:
1. What is the centroid of a triangle, and how is it located geometrically?
2. How does the centroid divide each median in terms of segment ratios?
3. If another median length was provided, how would that impact finding other segments?
4. What would change if \( D \) were not the centroid but a random point on the median?
5. How do properties of centroids extend to triangles in different coordinate planes?

**Tip:** Remember, the centroid is always located at the average of the vertices' coordinates in a coordinate plane, making it easy to calculate in coordinate geometry.

D is the centroid of triangle ABC. Find CE.

This solution explains how to find the length of CE in triangle ABC using centroid properties. Given that D is the centroid and ED is 12, the problem demonstrates how the centroid divides each median in a 2:1 ratio. Suitable for high school geometry students.

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